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Artificial neural network - Wikipedia
2001-10-02
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<div><p><a href="/wiki/File:Colored_neural_network.svg"></a></p><div><p>An artificial neural network is an interconnected group of nodes, inspired by a simplification of <a href="/wiki/Neuron">neurons</a> in a <a href="/wiki/Brain">brain</a>. Here, each circular node represents an <a href="/wiki/Artificial_neuron">artificial neuron</a> and an arrow represents a connection from the output of one artificial neuron to the input of another.</p></div></div>
<p><b>Artificial neural networks</b> (<b>ANNs</b>), usually simply called <b>neural networks</b> (<b>NNs</b>) or <b>neural nets</b>,<sup><a href="#cite_note-1">[1]</a></sup> are computing systems inspired by the <a href="/wiki/Biological_neural_network">biological neural networks</a> that constitute animal <a href="/wiki/Brain">brains</a>.<sup><a href="#cite_note-2">[2]</a></sup>
</p><p>An ANN is based on a collection of connected units or nodes called <a href="/wiki/Artificial_neuron">artificial neurons</a>, which loosely model the <a href="/wiki/Neuron">neurons</a> in a biological brain. Each connection, like the <a href="/wiki/Synapse">synapses</a> in a biological brain, can transmit a signal to other neurons. An artificial neuron receives signals then processes them and can signal neurons connected to it. The "signal" at a connection is a <a href="/wiki/Real_number">real number</a>, and the output of each neuron is computed by some non-linear function of the sum of its inputs. The connections are called <i>edges</i>. Neurons and edges typically have a <i><a href="/wiki/Weighting">weight</a></i> that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Neurons may have a threshold such that a signal is sent only if the aggregate signal crosses that threshold.
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Typically, neurons are aggregated into layers. Different layers may perform different transformations on their inputs. Signals travel from the first layer (the input layer), to the last layer (the output layer), possibly after traversing the layers multiple times.</p>
<h2>Training[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=1">edit</a>]</h2>
<p><a href="/wiki/Neural_network">Neural networks</a> learn (or are trained) by processing examples, each of which contains a known "input" and "result," forming probability-weighted associations between the two, which are stored within the data structure of the net itself. The training of a neural network from a given example is usually conducted by determining the difference between the processed output of the network (often a prediction) and a target output. This difference is the error. The network then adjusts its weighted associations according to a learning rule and using this error value. Successive adjustments will cause the neural network to produce output that is increasingly similar to the target output. After a sufficient number of these adjustments, the training can be terminated based on certain criteria. This is known as <a href="/wiki/Supervised_learning">supervised learning</a>.
</p><p>Such systems "learn" to perform tasks by considering examples, generally without being programmed with task-specific rules. For example, in <a href="/wiki/Image_recognition">image recognition</a>, they might learn to identify images that contain cats by analyzing example images that have been manually <a href="/wiki/Labeled_data">labeled</a> as "cat" or "no cat" and using the results to identify cats in other images. They do this without any prior knowledge of cats, for example, that they have fur, tails, whiskers, and cat-like faces. Instead, they automatically generate identifying characteristics from the examples that they process.
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<h2>History[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=2">edit</a>]</h2>
<p><a href="/wiki/Warren_McCulloch">Warren McCulloch</a> and <a href="/wiki/Walter_Pitts">Walter Pitts</a><sup><a href="#cite_note-3">[3]</a></sup> (1943) opened the subject by creating a computational model for neural networks.<sup><a href="#cite_note-4">[4]</a></sup> In the late 1940s, <a href="/wiki/Donald_O._Hebb">D. O. Hebb</a><sup><a href="#cite_note-5">[5]</a></sup> created a learning <a href="/wiki/Hypothesis">hypothesis</a> based on the mechanism of <a href="/wiki/Neuroplasticity">neural plasticity</a> that became known as <a href="/wiki/Hebbian_learning">Hebbian learning</a>. Farley and <a href="/wiki/Wesley_A._Clark">Wesley A. Clark</a><sup><a href="#cite_note-6">[6]</a></sup> (1954) first used computational machines, then called "calculators", to simulate a Hebbian network. In 1958, psychologist <a href="/wiki/Frank_Rosenblatt">Frank Rosenblatt</a> invented the <a href="/wiki/Perceptron">perceptron</a>, the first artificial neural network,<sup><a href="#cite_note-7">[7]</a></sup><sup><a href="#cite_note-8">[8]</a></sup><sup><a href="#cite_note-Werbos_1975-9">[9]</a></sup><sup><a href="#cite_note-10">[10]</a></sup> funded by the United States <a href="/wiki/Office_of_Naval_Research">Office of Naval Research</a>.<sup><a href="#cite_note-Olazaran-11">[11]</a></sup> The first functional networks with many layers were published by <a href="/wiki/Alexey_Grigorevich_Ivakhnenko">Ivakhnenko</a> and Lapa in 1965, as the <a href="/wiki/Group_method_of_data_handling">Group Method of Data Handling</a>.<sup><a href="#cite_note-SCHIDHUB2-12">[12]</a></sup><sup><a href="#cite_note-ivak1965-13">[13]</a></sup><sup><a href="#cite_note-ivak1967-14">[14]</a></sup> The basics of continuous backpropagation<sup><a href="#cite_note-SCHIDHUB2-12">[12]</a></sup><sup><a href="#cite_note-scholarpedia2-15">[15]</a></sup><sup><a href="#cite_note-:5-16">[16]</a></sup><sup><a href="#cite_note-mizutani2000-17">[17]</a></sup> were derived in the context of <a href="/wiki/Control_theory">control theory</a> by <a href="/wiki/Henry_J._Kelley">Kelley</a><sup><a href="#cite_note-kelley1960-18">[18]</a></sup> in 1960 and by <a href="/wiki/Arthur_E._Bryson">Bryson</a> in 1961,<sup><a href="#cite_note-bryson1961-19">[19]</a></sup> using principles of <a href="/wiki/Dynamic_programming">dynamic programming</a>. Thereafter research stagnated following <a href="/wiki/Marvin_Minsky">Minsky</a> and <a href="/wiki/Seymour_Papert">Papert</a> (1969),<sup><a href="#cite_note-20">[20]</a></sup> who discovered that basic perceptrons were incapable of processing the exclusive-or circuit and that computers lacked sufficient power to process useful neural networks.
</p><p>In 1970, <a href="/wiki/Seppo_Linnainmaa">Seppo Linnainmaa</a> published the general method for <a href="/wiki/Automatic_differentiation">automatic differentiation</a> (AD) of discrete connected networks of nested <a href="/wiki/Differentiable_function">differentiable</a> functions.<sup><a href="#cite_note-lin1970-21">[21]</a></sup><sup><a href="#cite_note-lin1976-22">[22]</a></sup> In 1973, Dreyfus used <a href="/wiki/Backpropagation">backpropagation</a> to adapt <a href="/wiki/Parameter">parameters</a> of controllers in proportion to error gradients.<sup><a href="#cite_note-dreyfus1973-23">[23]</a></sup> <a href="/wiki/Paul_Werbos">Werbos</a>'s (1975) <a href="/wiki/Backpropagation">backpropagation</a> algorithm enabled practical training of multi-layer networks. In 1982, he applied Linnainmaa's AD method to neural networks in the way that became widely used.<sup><a href="#cite_note-scholarpedia2-15">[15]</a></sup><sup><a href="#cite_note-werbos1982-24">[24]</a></sup>
</p><p>The development of <a href="/wiki/Metal%E2%80%93oxide%E2%80%93semiconductor">metal–oxide–semiconductor</a> (MOS) <a href="/wiki/Very-large-scale_integration">very-large-scale integration</a> (VLSI), in the form of <a href="/wiki/Complementary_MOS">complementary MOS</a> (CMOS) technology, enabled increasing MOS <a href="/wiki/Transistor_count">transistor counts</a> in <a href="/wiki/Digital_electronics">digital electronics</a>. This provided more processing power for the development of practical artificial neural networks in the 1980s.<sup><a href="#cite_note-Mead-25">[25]</a></sup>
</p><p>In 1986 <a href="/wiki/David_Rumelhart">Rumelhart</a>, <a href="/wiki/Geoffrey_Hinton">Hinton</a> and <a href="/wiki/Ronald_J._Williams">Williams</a> showed that backpropagation learned interesting internal representations of words as feature vectors when trained to predict the next word in a sequence.<sup><a href="#cite_note-RUMEL1986-26">[26]</a></sup>
</p><p>From 1988 onward,<sup><a href="#cite_note-Qian1988-27">[27]</a></sup><sup><a href="#cite_note-Bohr1988-28">[28]</a></sup> the use of neural networks transformed the field of protein structure prediction, in particular when the first cascading networks were trained on <i>profiles</i> (matrices) produced by multiple sequence alignments.<sup><a href="#cite_note-Rost1993-29">[29]</a></sup>
</p><p>In 1992, <a href="/wiki/Convolutional_neural_network#Pooling_layer">max-pooling</a> was introduced to help with least-shift invariance and tolerance to deformation to aid <a href="/wiki/3D_object_recognition">3D object recognition</a>.<sup><a href="#cite_note-Weng1992-30">[30]</a></sup><sup><a href="#cite_note-Weng19932-31">[31]</a></sup><sup><a href="#cite_note-Weng1997-32">[32]</a></sup> <a href="/wiki/J%C3%BCrgen_Schmidhuber">Schmidhuber</a> adopted a multi-level hierarchy of networks (1992) pre-trained one level at a time by <a href="/wiki/Unsupervised_learning">unsupervised learning</a> and fine-tuned by <a href="/wiki/Backpropagation">backpropagation</a>.<sup><a href="#cite_note-SCHMID1992-33">[33]</a></sup>
</p><p>Neural networks' early successes included predicting the stock market and in 1995 a (mostly) self-driving car.<sup><a href="#cite_note-34">[a]</a></sup><sup><a href="#cite_note-35">[34]</a></sup>
</p><p><a href="/wiki/Geoffrey_Hinton">Geoffrey Hinton</a> et al. (2006) proposed learning a high-level representation using successive layers of binary or real-valued <a href="/wiki/Latent_variable">latent variables</a> with a <a href="/wiki/Restricted_Boltzmann_machine">restricted Boltzmann machine</a><sup><a href="#cite_note-smolensky1986-36">[35]</a></sup> to model each layer. In 2012, <a href="/wiki/Andrew_Ng">Ng</a> and <a href="/wiki/Jeff_Dean_(computer_scientist)">Dean</a> created a network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images.<sup><a href="#cite_note-ng2012-37">[36]</a></sup> Unsupervised pre-training and increased computing power from <a href="/wiki/GPU">GPUs</a> and <a href="/wiki/Distributed_computing">distributed computing</a> allowed the use of larger networks, particularly in image and visual recognition problems, which became known as "<a href="/wiki/Deep_learning">deep learning</a>".<sup><a href="#cite_note-38">[37]</a></sup>
</p><p>Ciresan and colleagues (2010)<sup><a href="#cite_note-:3-39">[38]</a></sup> showed that despite the <a href="/wiki/Vanishing_gradient_problem">vanishing gradient problem</a>, GPUs make backpropagation feasible for many-layered feedforward neural networks.<sup><a href="#cite_note-Scherer2010-40">[39]</a></sup> Between 2009 and 2012, ANNs began winning prizes in image recognition contests, approaching human level performance on various tasks, initially in <a href="/wiki/Pattern_recognition">pattern recognition</a> and <a href="/wiki/Handwriting_recognition">handwriting recognition</a>.<sup><a href="#cite_note-41">[40]</a></sup><sup><a href="#cite_note-42">[41]</a></sup> For example, the bi-directional and multi-dimensional <a href="/wiki/Long_short-term_memory">long short-term memory</a> (LSTM)<sup><a href="#cite_note-graves20093-43">[42]</a></sup><sup><a href="#cite_note-graves_855-44">[43]</a></sup> of <a href="/wiki/Alex_Graves_(computer_scientist)">Graves</a> et al. won three competitions in connected handwriting recognition in 2009 without any prior knowledge about the three languages to be learned.<sup><a href="#cite_note-graves20093-43">[42]</a></sup><sup><a href="#cite_note-graves_855-44">[43]</a></sup>
</p><p>Ciresan and colleagues built the first pattern recognizers to achieve human-competitive/superhuman performance<sup><a href="#cite_note-45">[44]</a></sup> on benchmarks such as traffic sign recognition (IJCNN 2012).
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<h2>Models[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=3">edit</a>]</h2>
<div><p><a href="/wiki/File:Neuron3.png"></a></p><div><p>Neuron and myelinated axon, with signal flow from inputs at dendrites to outputs at axon terminals</p></div></div>
<p>ANNs began as an attempt to exploit the architecture of the human brain to perform tasks that conventional algorithms had little success with. They soon reoriented towards improving empirical results, mostly abandoning attempts to remain true to their biological precursors. Neurons are connected to each other in various patterns, to allow the output of some neurons to become the input of others. The network forms a <a href="/wiki/Directed_graph">directed</a>, <a href="/wiki/Weighted_graph">weighted graph</a>.<sup><a href="#cite_note-Zell1994ch5.2-46">[45]</a></sup>
</p><p>An artificial neural network consists of a collection of simulated neurons. Each neuron is a <a href="/wiki/Vertex_(graph_theory)">node</a> which is connected to other nodes via <a href="/wiki/Glossary_of_graph_theory_terms#edge">links</a> that correspond to biological axon-synapse-dendrite connections. Each link has a weight, which determines the strength of one node's influence on another.<sup><a href="#cite_note-Winston-47">[46]</a></sup>
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<h3>Artificial neurons[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=4">edit</a>]</h3>
<p>ANNs are composed of <a href="/wiki/Artificial_neurons">artificial neurons</a> which are conceptually derived from biological <a href="/wiki/Neuron">neurons</a>. Each artificial neuron has inputs and produces a single output which can be sent to multiple other neurons.<sup><a href="#cite_note-Abbod2007-48">[47]</a></sup> The inputs can be the feature values of a sample of external data, such as images or documents, or they can be the outputs of other neurons. The outputs of the final <i>output neurons</i> of the neural net accomplish the task, such as recognizing an object in an image.
</p><p>To find the output of the neuron we take the weighted sum of all the inputs, weighted by the <i>weights</i> of the <i>connections</i> from the inputs to the neuron. We add a <i>bias</i> term to this sum.<sup><a href="#cite_note-DAWSON1998-49">[48]</a></sup> This weighted sum is sometimes called the <i>activation</i>. This weighted sum is then passed through a (usually nonlinear) <a href="/wiki/Activation_function">activation function</a> to produce the output. The initial inputs are external data, such as images and documents. The ultimate outputs accomplish the task, such as recognizing an object in an image.<sup><a href="#cite_note-50">[49]</a></sup>
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<h3>Organization[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=5">edit</a>]</h3>
<p>The neurons are typically organized into multiple layers, especially in <a href="/wiki/Deep_learning">deep learning</a>. Neurons of one layer connect only to neurons of the immediately preceding and immediately following layers. The layer that receives external data is the <i>input layer</i>. The layer that produces the ultimate result is the <i>output layer</i>. In between them are zero or more <i>hidden layers</i>. Single layer and unlayered networks are also used. Between two layers, multiple connection patterns are possible. They can be 'fully connected', with every neuron in one layer connecting to every neuron in the next layer. They can be <i>pooling</i>, where a group of neurons in one layer connect to a single neuron in the next layer, thereby reducing the number of neurons in that layer.<sup><a href="#cite_note-flexible-51">[50]</a></sup> Neurons with only such connections form a <a href="/wiki/Directed_acyclic_graph">directed acyclic graph</a> and are known as <a href="/wiki/Feedforward_neural_network"><i>feedforward networks</i></a>.<sup><a href="#cite_note-Zell1994p73-52">[51]</a></sup> Alternatively, networks that allow connections between neurons in the same or previous layers are known as <a href="/wiki/Recurrent_neural_network"><i>recurrent networks</i></a><i>.<sup><a href="#cite_note-53">[52]</a></sup></i>
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<h3>Hyperparameter[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=6">edit</a>]</h3>
<p>A <a href="/wiki/Hyperparameter">hyperparameter</a> is a constant <a href="/wiki/Parameter">parameter</a> whose value is set before the learning process begins. The values of <a href="/wiki/Parameter">parameters</a> are derived via learning. Examples of hyperparameters include <a href="/wiki/Learning_rate">learning rate</a>, the number of hidden layers and batch size.<sup><a href="#cite_note-54">[53]</a></sup> The values of some hyperparameters can be dependent on those of other hyperparameters. For example, the size of some layers can depend on the overall number of layers.
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<h3>Learning[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=7">edit</a>]</h3>
<p>Learning is the adaptation of the network to better handle a task by considering sample observations. Learning involves adjusting the weights (and optional thresholds) of the network to improve the accuracy of the result. This is done by minimizing the observed errors. Learning is complete when examining additional observations does not usefully reduce the error rate. Even after learning, the error rate typically does not reach 0. If after learning, the error rate is too high, the network typically must be redesigned. Practically this is done by defining a <a href="/wiki/Loss_function">cost function</a> that is evaluated periodically during learning. As long as its output continues to decline, learning continues. The cost is frequently defined as a <a href="/wiki/Statistic">statistic</a> whose value can only be approximated. The outputs are actually numbers, so when the error is low, the difference between the output (almost certainly a cat) and the correct answer (cat) is small. Learning attempts to reduce the total of the differences across the observations. Most learning models can be viewed as a straightforward application of <a href="/wiki/Mathematical_optimization">optimization</a> theory and <a href="/wiki/Statistical_estimation">statistical estimation</a>.<sup><a href="#cite_note-Zell1994ch5.2-46">[45]</a></sup><sup><a href="#cite_note-55">[54]</a></sup>
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<h4>Learning rate[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=8">edit</a>]</h4>
<p>The learning rate defines the size of the corrective steps that the model takes to adjust for errors in each observation.<sup><a href="#cite_note-56">[55]</a></sup> A high learning rate shortens the training time, but with lower ultimate accuracy, while a lower learning rate takes longer, but with the potential for greater accuracy. Optimizations such as <a href="/wiki/Quickprop">Quickprop</a> are primarily aimed at speeding up error minimization, while other improvements mainly try to increase reliability. In order to avoid <a href="/wiki/Oscillation">oscillation</a> inside the network such as alternating connection weights, and to improve the rate of convergence, refinements use an <a href="/wiki/Adaptive_learning_rate">adaptive learning rate</a> that increases or decreases as appropriate.<sup><a href="#cite_note-57">[56]</a></sup> The concept of momentum allows the balance between the gradient and the previous change to be weighted such that the weight adjustment depends to some degree on the previous change. A momentum close to 0 emphasizes the gradient, while a value close to 1 emphasizes the last change.
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<h4>Cost function[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=9">edit</a>]</h4>
<p>While it is possible to define a cost function <a href="/wiki/Ad_hoc">ad hoc</a>, frequently the choice is determined by the function's desirable properties (such as <a href="/wiki/Convex_function">convexity</a>) or because it arises from the model (e.g. in a probabilistic model the model's <a href="/wiki/Posterior_probability">posterior probability</a> can be used as an inverse cost).
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<h4>Backpropagation[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=10">edit</a>]</h4>
<p>Backpropagation is a method used to adjust the connection weights to compensate for each error found during learning. The error amount is effectively divided among the connections. Technically, backprop calculates the <a href="/wiki/Gradient">gradient</a> (the derivative) of the <a href="/wiki/Loss_function">cost function</a> associated with a given state with respect to the weights. The weight updates can be done via <a href="/wiki/Stochastic_gradient_descent">stochastic gradient descent</a> or other methods, such as <a href="/wiki/Extreme_Learning_Machines">Extreme Learning Machines</a>,<sup><a href="#cite_note-58">[57]</a></sup> "No-prop" networks,<sup><a href="#cite_note-59">[58]</a></sup> training without backtracking,<sup><a href="#cite_note-60">[59]</a></sup> "weightless" networks,<sup><a href="#cite_note-RBMTRAIN-61">[60]</a></sup><sup><a href="#cite_note-62">[61]</a></sup> and <a href="/wiki/Holographic_associative_memory">non-connectionist neural networks</a>.<sup>[<i><a href="/wiki/Wikipedia:Citation_needed">citation needed</a></i>]</sup>
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<h3>Learning paradigms[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=11">edit</a>]</h3>
<p>Machine learning is commonly separated into three main learning paradigms, <a href="/wiki/Supervised_learning">supervised learning</a>, <a href="/wiki/Unsupervised_learning">unsupervised learning</a> and <a href="/wiki/Reinforcement_learning">reinforcement learning</a>.<sup><a href="#cite_note-63">[62]</a></sup> Each corresponds to a particular learning task.
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<h4>Supervised learning[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=12">edit</a>]</h4>
<p><a href="/wiki/Supervised_learning">Supervised learning</a> uses a set of paired inputs and desired outputs. The learning task is to produce the desired output for each input. In this case, the cost function is related to eliminating incorrect deductions.<sup><a href="#cite_note-64">[63]</a></sup> A commonly used cost is the <a href="/wiki/Mean-squared_error">mean-squared error</a>, which tries to minimize the average squared error between the network's output and the desired output. Tasks suited for supervised learning are <a href="/wiki/Pattern_recognition">pattern recognition</a> (also known as classification) and <a href="/wiki/Regression_analysis">regression</a> (also known as function approximation). Supervised learning is also applicable to sequential data (e.g., for hand writing, speech and <a href="/wiki/Gesture_recognition">gesture recognition</a>). This can be thought of as learning with a "teacher", in the form of a function that provides continuous feedback on the quality of solutions obtained thus far.
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<h4>Unsupervised learning[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=13">edit</a>]</h4>
<p>In <a href="/wiki/Unsupervised_learning">unsupervised learning</a>, input data is given along with the cost function, some function of the data and the network's output. The cost function is dependent on the task (the model domain) and any <i><a href="/wiki/A_priori_and_a_posteriori">a priori</a></i> assumptions (the implicit properties of the model, its parameters and the observed variables). As a trivial example, consider the model where is a constant and the cost . Minimizing this cost produces a value of that is equal to the mean of the data. The cost function can be much more complicated. Its form depends on the application: for example, in <a href="/wiki/Data_compression">compression</a> it could be related to the <a href="/wiki/Mutual_information">mutual information</a> between and , whereas in statistical modeling, it could be related to the <a href="/wiki/Posterior_probability">posterior probability</a> of the model given the data (note that in both of those examples, those quantities would be maximized rather than minimized). Tasks that fall within the paradigm of unsupervised learning are in general <a href="/wiki/Approximation">estimation</a> problems; the applications include <a href="/wiki/Data_clustering">clustering</a>, the estimation of <a href="/wiki/Statistical_distributions">statistical distributions</a>, <a href="/wiki/Data_compression">compression</a> and <a href="/wiki/Bayesian_spam_filtering">filtering</a>.
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<h4>Reinforcement learning[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=14">edit</a>]</h4>
<p>In applications such as playing video games, an actor takes a string of actions, receiving a generally unpredictable response from the environment after each one. The goal is to win the game, i.e., generate the most positive (lowest cost) responses. In <a href="/wiki/Reinforcement_learning">reinforcement learning</a>, the aim is to weight the network (devise a policy) to perform actions that minimize long-term (expected cumulative) cost. At each point in time the agent performs an action and the environment generates an observation and an <a href="/wiki/Instant">instantaneous</a> cost, according to some (usually unknown) rules. The rules and the long-term cost usually only can be estimated. At any juncture, the agent decides whether to explore new actions to uncover their costs or to exploit prior learning to proceed more quickly.
</p><p>Formally the environment is modeled as a <a href="/wiki/Markov_decision_process">Markov decision process</a> (MDP) with states and actions . Because the state transitions are not known, probability distributions are used instead: the instantaneous cost distribution , the observation distribution and the transition distribution , while a policy is defined as the conditional distribution over actions given the observations. Taken together, the two define a <a href="/wiki/Markov_chain">Markov chain</a> (MC). The aim is to discover the lowest-cost MC.
</p><p>ANNs serve as the learning component in such applications.<sup><a href="#cite_note-65">[64]</a></sup><sup><a href="#cite_note-66">[65]</a></sup> <a href="/wiki/Dynamic_programming">Dynamic programming</a> coupled with ANNs (giving <a href="/wiki/Neural_oscillation">neurodynamic</a> programming)<sup><a href="#cite_note-67">[66]</a></sup> has been applied to problems such as those involved in <a href="/wiki/Vehicle_routing">vehicle routing</a>,<sup><a href="#cite_note-68">[67]</a></sup> video games, <a href="/wiki/Natural_resource_management">natural resource management</a><sup><a href="#cite_note-69">[68]</a></sup><sup><a href="#cite_note-70">[69]</a></sup> and <a href="/wiki/Medicine">medicine</a><sup><a href="#cite_note-71">[70]</a></sup> because of ANNs ability to mitigate losses of accuracy even when reducing the <a href="/wiki/Discretization">discretization</a> grid density for numerically approximating the solution of control problems. Tasks that fall within the paradigm of reinforcement learning are control problems, <a href="/wiki/Game">games</a> and other sequential decision making tasks.
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<h4>Self-learning[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=15">edit</a>]</h4>
<p>Self-learning in neural networks was introduced in 1982 along with a neural network capable of self-learning named Crossbar Adaptive Array (CAA).<sup><a href="#cite_note-72">[71]</a></sup> It is a system with only one input, situation s, and only one output, action (or behavior) a. It has neither external advice input nor external reinforcement input from the environment. The CAA computes, in a crossbar fashion, both decisions about actions and emotions (feelings) about encountered situations. The system is driven by the interaction between cognition and emotion.<sup><a href="#cite_note-73">[72]</a></sup> Given the memory matrix, W =||w(a,s)||, the crossbar self-learning algorithm in each iteration performs the following computation:
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<pre> In situation s perform action a;
 Receive consequence situation s';
 Compute emotion of being in consequence situation v(s');
 Update crossbar memory w'(a,s) = w(a,s) + v(s').
</pre>
<p>The backpropagated value (secondary reinforcement) is the emotion toward the consequence situation. The CAA exists in two environments, one is behavioral environment where it behaves, and the other is genetic environment, where from it initially and only once receives initial emotions about to be encountered situations in the behavioral environment. Having received the genome vector (species vector) from the genetic environment, the CAA will learn a goal-seeking behavior, in the behavioral environment that contains both desirable and undesirable situations.<sup><a href="#cite_note-74">[73]</a></sup>
</p>
<h4>Neuroevolution[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=16">edit</a>]</h4>
<p><a href="/wiki/Neuroevolution">Neuroevolution</a> can create neural network topologies and weights using <a href="/wiki/Evolutionary_computation">evolutionary computation</a>. It is competitive with sophisticated gradient descent approaches<sup>[<i><a href="/wiki/Wikipedia:Citation_needed">citation needed</a></i>]</sup>. One advantage of neuroevolution is that it may be less prone to get caught in "dead ends".<sup><a href="#cite_note-75">[74]</a></sup>
</p>
<h3>Stochastic neural network[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=17">edit</a>]</h3>
<p><b>Stochastic neural networks</b> originating from <a href="/wiki/Spin_glass#Sherrington–Kirkpatrick_model">Sherrington–Kirkpatrick models</a> are a type of artificial neural network built by introducing random variations into the network, either by giving the network's <a href="/wiki/Artificial_neuron">artificial neurons</a> <a href="/wiki/Stochastic_process">stochastic</a> transfer functions, or by giving them stochastic weights. This makes them useful tools for <a href="/wiki/Optimization_(mathematics)">optimization</a> problems, since the random fluctuations help the network escape from <a href="/wiki/Maxima_and_minima">local minima</a>.<sup><a href="#cite_note-76">[75]</a></sup> Stochastic neural networks trained using a Bayesian approach are known as <b>Bayesian neural networks</b>.<sup><a href="#cite_note-77">[76]</a></sup>
</p>
<h3>Other[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=18">edit</a>]</h3>
<p>In a <a href="/wiki/Bayesian_probability">Bayesian</a> framework, a distribution over the set of allowed models is chosen to minimize the cost. <a href="/wiki/Evolutionary_methods">Evolutionary methods</a>,<sup><a href="#cite_note-78">[77]</a></sup> <a href="/wiki/Gene_expression_programming">gene expression programming</a>,<sup><a href="#cite_note-79">[78]</a></sup> <a href="/wiki/Simulated_annealing">simulated annealing</a>,<sup><a href="#cite_note-80">[79]</a></sup> <a href="/wiki/Expectation-maximization">expectation-maximization</a>, <a href="/wiki/Non-parametric_methods">non-parametric methods</a> and <a href="/wiki/Particle_swarm_optimization">particle swarm optimization</a><sup><a href="#cite_note-81">[80]</a></sup> are other learning algorithms. Convergent recursion is a learning algorithm for <a href="/wiki/Cerebellar_model_articulation_controller">cerebellar model articulation controller</a> (CMAC) neural networks.<sup><a href="#cite_note-Qin1-82">[81]</a></sup><sup><a href="#cite_note-Qin2-83">[82]</a></sup>
</p>
<h4>Modes[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=19">edit</a>]</h4>
<p>Two modes of learning are available: <a href="/wiki/Stochastic_gradient_descent">stochastic</a> and batch. In stochastic learning, each input creates a weight adjustment. In batch learning weights are adjusted based on a batch of inputs, accumulating errors over the batch. Stochastic learning introduces "noise" into the process, using the local gradient calculated from one data point; this reduces the chance of the network getting stuck in local minima. However, batch learning typically yields a faster, more stable descent to a local minimum, since each update is performed in the direction of the batch's average error. A common compromise is to use "mini-batches", small batches with samples in each batch selected stochastically from the entire data set.
</p>
<h2>Types[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=20">edit</a>]</h2>
<p>ANNs have evolved into a broad family of techniques that have advanced the state of the art across multiple domains. The simplest types have one or more static components, including number of units, number of layers, unit weights and <a href="/wiki/Topology">topology</a>. Dynamic types allow one or more of these to evolve via learning. The latter are much more complicated, but can shorten learning periods and produce better results. Some types allow/require learning to be "supervised" by the operator, while others operate independently. Some types operate purely in hardware, while others are purely software and run on general purpose computers.
</p><p>Some of the main breakthroughs include: <a href="/wiki/Convolutional_neural_network">convolutional neural networks</a> that have proven particularly successful in processing visual and other two-dimensional data;<sup><a href="#cite_note-LECUN1989-84">[83]</a></sup><sup><a href="#cite_note-lecun2016slides-85">[84]</a></sup> long short-term memory avoid the <a href="/wiki/Vanishing_gradient_problem">vanishing gradient problem</a><sup><a href="#cite_note-:03-86">[85]</a></sup> and can handle signals that have a mix of low and high frequency components aiding large-vocabulary speech recognition,<sup><a href="#cite_note-sak2014-87">[86]</a></sup><sup><a href="#cite_note-liwu2015-88">[87]</a></sup> text-to-speech synthesis,<sup><a href="#cite_note-89">[88]</a></sup><sup><a href="#cite_note-scholarpedia2-15">[15]</a></sup><sup><a href="#cite_note-zen2015-90">[89]</a></sup> and photo-real talking heads;<sup><a href="#cite_note-fan2015-91">[90]</a></sup> competitive networks such as <a href="/wiki/Generative_adversarial_network">generative adversarial networks</a> in which multiple networks (of varying structure) compete with each other, on tasks such as winning a game<sup><a href="#cite_note-preprint-92">[91]</a></sup> or on deceiving the opponent about the authenticity of an input.<sup><a href="#cite_note-GANnips-93">[92]</a></sup>
</p>
<h2>Network design[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=21">edit</a>]</h2>
<p>Neural architecture search (NAS) uses machine learning to automate ANN design. Various approaches to NAS have designed networks that compare well with hand-designed systems. The basic search algorithm is to propose a candidate model, evaluate it against a dataset and use the results as feedback to teach the NAS network.<sup><a href="#cite_note-94">[93]</a></sup> Available systems include <a href="/wiki/Automated_machine_learning">AutoML</a> and AutoKeras.<sup><a href="#cite_note-95">[94]</a></sup>
</p><p>Design issues include deciding the number, type and connectedness of network layers, as well as the size of each and the connection type (full, pooling, ...).
</p><p><a href="/wiki/Hyperparameter">Hyperparameters</a> must also be defined as part of the design (they are not learned), governing matters such as how many neurons are in each layer, learning rate, step, stride, depth, receptive field and padding (for CNNs), etc.<sup><a href="#cite_note-abs1502.02127-96">[95]</a></sup>
</p>
<h2>Use[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=22">edit</a>]</h2>
<p>Using Artificial neural networks requires an understanding of their characteristics.
</p>
<ul><li>Choice of model: This depends on the data representation and the application. Overly complex models are slow learning.</li>
<li>Learning algorithm: Numerous trade-offs exist between learning algorithms. Almost any algorithm will work well with the correct <a href="/wiki/Hyperparameter">hyperparameters</a> for training on a particular data set. However, selecting and tuning an algorithm for training on unseen data requires significant experimentation.</li>
<li>Robustness: If the model, cost function and learning algorithm are selected appropriately, the resulting ANN can become robust.</li></ul>
<p>ANN capabilities fall within the following broad categories:<sup>[<i><a href="/wiki/Wikipedia:Citation_needed">citation needed</a></i>]</sup>
</p>
<ul><li><a href="/wiki/Function_approximation">Function approximation</a>, or <a href="/wiki/Regression_analysis">regression analysis</a>, including <a href="/wiki/Time_series#Prediction_and_forecasting">time series prediction</a>, <a href="/wiki/Fitness_approximation">fitness approximation</a> and modeling.</li>
<li><a href="/wiki/Statistical_classification">Classification</a>, including <a href="/wiki/Pattern_recognition">pattern</a> and sequence recognition, <a href="/wiki/Novelty_detection">novelty detection</a> and sequential decision making.<sup><a href="#cite_note-TurekNeuralNet-97">[96]</a></sup></li>
<li><a href="/wiki/Data_processing">Data processing</a>, including filtering, clustering, <a href="/wiki/Blind_source_separation">blind source separation</a> and compression.</li>
<li><a href="/wiki/Robotics">Robotics</a>, including directing manipulators and <a href="/wiki/Prosthesis">prostheses</a>.</li></ul>
<h2>Applications[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=23">edit</a>]</h2>
<p>Because of their ability to reproduce and model nonlinear processes, artificial neural networks have found applications in many disciplines. Application areas include <a href="/wiki/System_identification">system identification</a> and control (vehicle control, trajectory prediction,<sup><a href="#cite_note-98">[97]</a></sup> <a href="/wiki/Process_control">process control</a>, <a href="/wiki/Natural_resource_management">natural resource management</a>), <a href="/wiki/Quantum_chemistry">quantum chemistry</a>,<sup><a href="#cite_note-Balabin_2009-99">[98]</a></sup> <a href="/wiki/General_game_playing">general game playing</a>,<sup><a href="#cite_note-100">[99]</a></sup> <a href="/wiki/Pattern_recognition">pattern recognition</a> (radar systems, <a href="/wiki/Facial_recognition_system">face identification</a>, signal classification,<sup><a href="#cite_note-101">[100]</a></sup> <a href="/wiki/3D_reconstruction">3D reconstruction</a>,<sup><a href="#cite_note-102">[101]</a></sup> object recognition and more), sensor data analysis,<sup><a href="#cite_note-103">[102]</a></sup> sequence recognition (gesture, speech, <a href="/wiki/Handwriting_recognition">handwritten</a> and printed text recognition<sup><a href="#cite_note-104">[103]</a></sup>), <a href="/wiki/Medical_diagnosis">medical diagnosis</a>, finance<sup><a href="#cite_note-105">[104]</a></sup> (e.g. <a href="/wiki/Algorithmic_trading">automated trading systems</a>), <a href="/wiki/Data_mining">data mining</a>, visualization, <a href="/wiki/Machine_translation">machine translation</a>, social network filtering<sup><a href="#cite_note-106">[105]</a></sup> and <a href="/wiki/E-mail_spam">e-mail spam</a> filtering. ANNs have been used to diagnose several types of cancers<sup><a href="#cite_note-107">[106]</a></sup><sup><a href="#cite_note-108">[107]</a></sup> and to distinguish highly invasive cancer cell lines from less invasive lines using only cell shape information.<sup><a href="#cite_note-109">[108]</a></sup><sup><a href="#cite_note-110">[109]</a></sup>
</p><p>ANNs have been used to accelerate reliability analysis of infrastructures subject to natural disasters<sup><a href="#cite_note-111">[110]</a></sup><sup><a href="#cite_note-112">[111]</a></sup> and to predict foundation settlements.<sup><a href="#cite_note-113">[112]</a></sup> ANNs have also been used for building black-box models in <a href="/wiki/Geoscience">geoscience</a>: <a href="/wiki/Hydrology">hydrology</a>,<sup><a href="#cite_note-114">[113]</a></sup><sup><a href="#cite_note-115">[114]</a></sup> ocean modelling and <a href="/wiki/Coastal_engineering">coastal engineering</a>,<sup><a href="#cite_note-116">[115]</a></sup><sup><a href="#cite_note-117">[116]</a></sup> and <a href="/wiki/Geomorphology">geomorphology</a>.<sup><a href="#cite_note-118">[117]</a></sup> ANNs have been employed in <a href="/wiki/Computer_security">cybersecurity</a>, with the objective to discriminate between legitimate activities and malicious ones. For example, machine learning has been used for classifying Android malware,<sup><a href="#cite_note-119">[118]</a></sup> for identifying domains belonging to threat actors and for detecting URLs posing a security risk.<sup><a href="#cite_note-120">[119]</a></sup> Research is underway on ANN systems designed for penetration testing, for detecting botnets,<sup><a href="#cite_note-121">[120]</a></sup> credit cards frauds<sup><a href="#cite_note-122">[121]</a></sup> and network intrusions.
</p><p>ANNs have been proposed as a tool to solve <a href="/wiki/Partial_differential_equation">partial differential equations</a> in physics<sup><a href="#cite_note-123">[122]</a></sup><sup><a href="#cite_note-124">[123]</a></sup><sup><a href="#cite_note-125">[124]</a></sup> and simulate the properties of many-body <a href="/wiki/Open_quantum_system">open quantum systems</a>.<sup><a href="#cite_note-126">[125]</a></sup><sup><a href="#cite_note-127">[126]</a></sup><sup><a href="#cite_note-128">[127]</a></sup><sup><a href="#cite_note-129">[128]</a></sup> In brain research ANNs have studied short-term behavior of <a href="/wiki/Biological_neuron_models">individual neurons</a>,<sup><a href="#cite_note-130">[129]</a></sup> the dynamics of neural circuitry arise from interactions between individual neurons and how behavior can arise from abstract neural modules that represent complete subsystems. Studies considered long-and short-term plasticity of neural systems and their relation to learning and memory from the individual neuron to the system level.
</p>
<h2>Theoretical properties[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=24">edit</a>]</h2>
<h3>Computational power[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=25">edit</a>]</h3>
<p>The <a href="/wiki/Multilayer_perceptron">multilayer perceptron</a> is a <a href="/wiki/UTM_theorem">universal function</a> approximator, as proven by the <a href="/wiki/Universal_approximation_theorem">universal approximation theorem</a>. However, the proof is not constructive regarding the number of neurons required, the network topology, the weights and the learning parameters.
</p><p>A specific recurrent architecture with <a href="/wiki/Rational_number">rational</a>-valued weights (as opposed to full precision <a href="/wiki/Real_number">real number</a>-valued weights) has the power of a <a href="/wiki/Universal_Turing_Machine">universal Turing machine</a>,<sup><a href="#cite_note-131">[130]</a></sup> using a finite number of neurons and standard linear connections. Further, the use of <a href="/wiki/Irrational_number">irrational</a> values for weights results in a machine with <a href="/wiki/Hypercomputation">super-Turing</a> power.<sup><a href="#cite_note-132">[131]</a></sup>
</p>
<h3>Capacity[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=26">edit</a>]</h3>
<p>A model's "capacity" property corresponds to its ability to model any given function. It is related to the amount of information that can be stored in the network and to the notion of complexity.
Two notions of capacity are known by the community. The information capacity and the VC Dimension. The information capacity of a perceptron is intensively discussed in Sir David MacKay's book<sup><a href="#cite_note-auto-133">[132]</a></sup> which summarizes work by Thomas Cover.<sup><a href="#cite_note-134">[133]</a></sup> The capacity of a network of standard neurons (not convolutional) can be derived by four rules<sup><a href="#cite_note-135">[134]</a></sup> that derive from understanding a neuron as an <a href="/wiki/ADALINE">electrical element</a>. The information capacity captures the functions modelable by the network given any data as input. The second notion, is the <a href="/wiki/VC_dimension">VC dimension</a>. VC Dimension uses the principles of <a href="/wiki/Measure_theory">measure theory</a> and finds the maximum capacity under the best possible circumstances. This is, given input data in a specific form. As noted in,<sup><a href="#cite_note-auto-133">[132]</a></sup> the VC Dimension for arbitrary inputs is half the information capacity of a Perceptron. The VC Dimension for arbitrary points is sometimes referred to as Memory Capacity.<sup><a href="#cite_note-136">[135]</a></sup>
</p>
<h3>Convergence[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=27">edit</a>]</h3>
<p>Models may not consistently converge on a single solution, firstly because local minima may exist, depending on the cost function and the model. Secondly, the optimization method used might not guarantee to converge when it begins far from any local minimum. Thirdly, for sufficiently large data or parameters, some methods become impractical.
</p><p>Another issue worthy to mention is that training may cross some <a href="/wiki/Saddle_point">Saddle point</a> which may lead the convergence to the wrong direction.
</p><p>The convergence behavior of certain types of ANN architectures are more understood than others. When the width of network approaches to infinity, the ANN is well described by its first order Taylor expansion throughout training, and so inherits the convergence behavior of <a href="/wiki/Linear_model">affine models</a>.<sup><a href="#cite_note-137">[136]</a></sup><sup><a href="#cite_note-138">[137]</a></sup> Another example is when parameters are small, it is observed that ANNs often fits target functions from low to high frequencies. This behavior is referred to as the spectral bias, or frequency principle, of neural networks.<sup><a href="#cite_note-139">[138]</a></sup><sup><a href="#cite_note-140">[139]</a></sup><sup><a href="#cite_note-141">[140]</a></sup><sup><a href="#cite_note-142">[141]</a></sup> This phenomenon is the opposite to the behavior of some well studied iterative numerical schemes such as <a href="/wiki/Jacobi_method">Jacobi method</a>. Deeper neural networks have been observed to be more biased towards low frequency functions.<sup><a href="#cite_note-143">[142]</a></sup>
</p>
<h3>Generalization and statistics[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=28">edit</a>]</h3>
<p>Applications whose goal is to create a system that generalizes well to unseen examples, face the possibility of over-training. This arises in convoluted or over-specified systems when the network capacity significantly exceeds the needed free parameters. Two approaches address over-training. The first is to use <a href="/wiki/Cross-validation_(statistics)">cross-validation</a> and similar techniques to check for the presence of over-training and to select <a href="/wiki/Hyperparameters">hyperparameters</a> to minimize the generalization error.
</p><p>The second is to use some form of <i><a href="/wiki/Regularization_(mathematics)">regularization</a></i>. This concept emerges in a probabilistic (Bayesian) framework, where regularization can be performed by selecting a larger prior probability over simpler models; but also in statistical learning theory, where the goal is to minimize over two quantities: the 'empirical risk' and the 'structural risk', which roughly corresponds to the error over the training set and the predicted error in unseen data due to overfitting.
</p>
<div><p><a href="/wiki/File:Synapse_deployment.jpg"></a></p><div><p>Confidence analysis of a neural network</p></div></div>
<p>Supervised neural networks that use a <a href="/wiki/Mean_squared_error">mean squared error</a> (MSE) cost function can use formal statistical methods to determine the confidence of the trained model. The MSE on a validation set can be used as an estimate for variance. This value can then be used to calculate the <a href="/wiki/Confidence_interval">confidence interval</a> of network output, assuming a <a href="/wiki/Normal_distribution">normal distribution</a>. A confidence analysis made this way is statistically valid as long as the output <a href="/wiki/Probability_distribution">probability distribution</a> stays the same and the network is not modified.
</p><p>By assigning a <a href="/wiki/Softmax_activation_function">softmax activation function</a>, a generalization of the <a href="/wiki/Logistic_function">logistic function</a>, on the output layer of the neural network (or a softmax component in a component-based network) for categorical target variables, the outputs can be interpreted as posterior probabilities. This is useful in classification as it gives a certainty measure on classifications.
</p><p>The softmax activation function is:
</p>
<dl><dd></dd></dl>
<h2>Criticism[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=29">edit</a>]</h2>
<h3>Training[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=30">edit</a>]</h3>
<p>A common criticism of neural networks, particularly in robotics, is that they require too much training for real-world operation.<sup>[<i><a href="/wiki/Wikipedia:Citation_needed">citation needed</a></i>]</sup> Potential solutions include randomly shuffling training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections following an example, grouping examples in so-called mini-batches and/or introducing a recursive least squares algorithm for <a href="/wiki/Cerebellar_model_articulation_controller">CMAC</a>.<sup><a href="#cite_note-Qin1-82">[81]</a></sup>
</p>
<h3>Theory[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=31">edit</a>]</h3>
<p>A central claim<sup>[<i><a href="/wiki/Wikipedia:Citation_needed">citation needed</a></i>]</sup> of ANNs is that they embody new and powerful general principles for processing information. These principles are ill-defined. It is often claimed<sup>[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions">by whom?</a></i>]</sup> that they are <a href="/wiki/Emergent_properties">emergent</a> from the network itself. This allows simple statistical association (the basic function of artificial neural networks) to be described as learning or recognition. In 1997, <a href="/wiki/Alexander_Dewdney">Alexander Dewdney</a> commented that, as a result, artificial neural networks have a "something-for-nothing quality, one that imparts a peculiar aura of laziness and a distinct lack of curiosity about just how good these computing systems are. No human hand (or mind) intervenes; solutions are found as if by magic; and no one, it seems, has learned anything".<sup><a href="#cite_note-144">[143]</a></sup> One response to Dewdney is that neural networks handle many complex and diverse tasks, ranging from autonomously flying aircraft<sup><a href="#cite_note-145">[144]</a></sup> to detecting credit card fraud to mastering the game of <a href="/wiki/Go_(game)">Go</a>.
</p><p>Technology writer Roger Bridgman commented:
</p>
<blockquote><p>Neural networks, for instance, are in the dock not only because they have been hyped to high heaven, (what hasn't?) but also because you could create a successful net without understanding how it worked: the bunch of numbers that captures its behaviour would in all probability be "an opaque, unreadable table...valueless as a scientific resource".
</p><p>In spite of his emphatic declaration that science is not technology, Dewdney seems here to pillory neural nets as bad science when most of those devising them are just trying to be good engineers. An unreadable table that a useful machine could read would still be well worth having.<sup><a href="#cite_note-146">[145]</a></sup>
</p>
</blockquote>
<p>Biological brains use both shallow and deep circuits as reported by brain anatomy,<sup><a href="#cite_note-VanEssen1991-147">[146]</a></sup> displaying a wide variety of invariance. Weng<sup><a href="#cite_note-Weng2012-148">[147]</a></sup> argued that the brain self-wires largely according to signal statistics and therefore, a serial cascade cannot catch all major statistical dependencies.
</p>
<h3>Hardware[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=32">edit</a>]</h3>
<p>Large and effective neural networks require considerable computing resources.<sup><a href="#cite_note-:0-149">[148]</a></sup> While the brain has hardware tailored to the task of processing signals through a <a href="/wiki/Graph_(discrete_mathematics)">graph</a> of neurons, simulating even a simplified neuron on <a href="/wiki/Von_Neumann_architecture">von Neumann architecture</a> may consume vast amounts of <a href="/wiki/Random-access_memory">memory</a> and storage. Furthermore, the designer often needs to transmit signals through many of these connections and their associated neurons – which require enormous <a href="/wiki/Central_processing_unit">CPU</a> power and time.
</p><p><a href="/wiki/J%C3%BCrgen_Schmidhuber">Schmidhuber</a> noted that the resurgence of neural networks in the twenty-first century is largely attributable to advances in hardware: from 1991 to 2015, computing power, especially as delivered by <a href="/wiki/General-purpose_computing_on_graphics_processing_units">GPGPUs</a> (on <a href="/wiki/Graphics_processing_unit">GPUs</a>), has increased around a million-fold, making the standard backpropagation algorithm feasible for training networks that are several layers deeper than before.<sup><a href="#cite_note-SCHIDHUB2-12">[12]</a></sup> The use of accelerators such as <a href="/wiki/Field-programmable_gate_array">FPGAs</a> and GPUs can reduce training times from months to days.<sup><a href="#cite_note-:0-149">[148]</a></sup>
</p><p><a href="/wiki/Neuromorphic_engineering">Neuromorphic engineering</a> or a <a href="/wiki/Physical_neural_network">physical neural network</a> addresses the hardware difficulty directly, by constructing non-von-Neumann chips to directly implement neural networks in circuitry. Another type of chip optimized for neural network processing is called a <a href="/wiki/Tensor_Processing_Unit">Tensor Processing Unit</a>, or TPU.<sup><a href="#cite_note-150">[149]</a></sup>
</p>
<h3>Practical counterexamples[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=33">edit</a>]</h3>
<p>Analyzing what has been learned by an ANN is much easier than analyzing what has been learned by a biological neural network. Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering general principles that allow a learning machine to be successful. For example, local vs. non-local learning and shallow vs. deep architecture.<sup><a href="#cite_note-151">[150]</a></sup>
</p>
<h3>Hybrid approaches[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=34">edit</a>]</h3>
<p>Advocates of <a href="/wiki/Hybrid_neural_network">hybrid</a> models (combining neural networks and symbolic approaches) say that such a mixture can better capture the mechanisms of the human mind.<sup><a href="#cite_note-152">[151]</a></sup>
</p>
<h2>Gallery[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=35">edit</a>]</h2>
<ul>
	<li><div>
	<div><p><a href="/wiki/File:Single_layer_ann.svg"></a></p></div>
	<p>A single-layer feedforward artificial neural network. Arrows originating from are omitted for clarity. There are p inputs to this network and q outputs. In this system, the value of the qth output, would be calculated as .
</p>
	</div></li>
	<li><div>
	<div><p><a href="/wiki/File:Two_layer_ann.svg"></a></p></div>
	<p>A two-layer feedforward artificial neural network
</p>
	</div></li>
	<li><div>
	<div><p><a href="/wiki/File:Artificial_neural_network.svg"></a></p></div>
	<p>An artificial neural network
</p>
	</div></li>
	<li><div>
	<div><p><a href="/wiki/File:Ann_dependency_(graph).svg"></a></p></div>
	<p>An ANN dependency graph
</p>
	</div></li>
	<li><div>
	<div><p><a href="/wiki/File:Single-layer_feedforward_artificial_neural_network.png"></a></p></div>
	<p>A single-layer feedforward artificial neural network with 4 inputs, 6 hidden and 2 outputs. Given position state and direction outputs wheel based control values.
</p>
	</div></li>
	<li><div>
	<div><p><a href="/wiki/File:Two-layer_feedforward_artificial_neural_network.png"></a></p></div>
	<p>A two-layer feedforward artificial neural network with 8 inputs, 2x8 hidden and 2 outputs. Given position state, direction and other environment values outputs thruster based control values.
</p>
	</div></li>
	<li><div>
	<div><p><a href="/wiki/File:Cmac.jpg"></a></p></div>
	<p>Parallel pipeline structure of CMAC neural network. This learning algorithm can converge in one step.
</p>
	</div></li>
</ul>
<h2>See also[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=36">edit</a>]</h2>
<div>
<ul><li><a href="/wiki/ADALINE">ADALINE</a></li>
<li>Artificial philosophy</li>
<li><a href="/wiki/Autoencoder">Autoencoder</a></li>
<li><a href="/wiki/Bio-inspired_computing">Bio-inspired computing</a></li>
<li><a href="/wiki/Blue_Brain_Project">Blue Brain Project</a></li>
<li><a href="/wiki/Catastrophic_interference">Catastrophic interference</a></li>
<li><a href="/wiki/Cognitive_architecture">Cognitive architecture</a></li>
<li><a href="/wiki/Connectionist_expert_system">Connectionist expert system</a></li>
<li><a href="/wiki/Connectomics">Connectomics</a></li>
<li><a href="/wiki/Large_width_limits_of_neural_networks">Large width limits of neural networks</a></li>
<li><a href="/wiki/List_of_machine_learning_concepts">List of machine learning concepts</a></li>
<li><a href="/wiki/Neural_gas">Neural gas</a></li>
<li><a href="/wiki/Neural_network_software">Neural network software</a></li>
<li><a href="/wiki/Optical_neural_network">Optical neural network</a></li>
<li><a href="/wiki/Parallel_distributed_processing">Parallel distributed processing</a></li>
<li><a href="/wiki/Recurrent_neural_networks">Recurrent neural networks</a></li>
<li><a href="/wiki/Spiking_neural_network">Spiking neural network</a></li>
<li><a href="/wiki/Tensor_product_network">Tensor product network</a></li></ul>
</div>
<h2>Notes[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=37">edit</a>]</h2>
<div><ol>
<li><b><a href="#cite_ref-34">^</a></b> Steering for the 1995 "<a href="/wiki/History_of_autonomous_cars#1990s">No Hands Across America</a>" required "only a few human assists".
</li>
</ol></div>
<h2>References[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=38">edit</a>]</h2>
<div>
<ol>
<li><b><a href="#cite_ref-1">^</a></b> <cite>Hardesty, Larry (14 April 2017). <a href="https://news.mit.edu/2017/explained-neural-networks-deep-learning-0414">"Explained: Neural networks"</a>. MIT News Office. Retrieved 2 June 2022.</cite>
</li>
<li><b><a href="#cite_ref-2">^</a></b> <cite>Yang, Z.R.; Yang, Z. (2014). <a href="https://www.sciencedirect.com/topics/neuroscience/artificial-neural-network"><i>Comprehensive Biomedical Physics</i></a>. Karolinska Institute, Stockholm, Sweden: Elsevier. p. 1. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-444-53633-4"><bdi>978-0-444-53633-4</bdi></a>. <a href="https://web.archive.org/web/20220728183237/https://www.sciencedirect.com/topics/neuroscience/artificial-neural-network">Archived</a> from the original on 28 July 2022. Retrieved 28 July 2022.</cite>
</li>
<li><b><a href="#cite_ref-3">^</a></b> <cite>McCulloch, Warren; Walter Pitts (1943). "A Logical Calculus of Ideas Immanent in Nervous Activity". <i>Bulletin of Mathematical Biophysics</i>. <b>5</b> (4): 115–133. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2FBF02478259">10.1007/BF02478259</a>.</cite>
</li>
<li><b><a href="#cite_ref-4">^</a></b> <cite>Kleene, S.C. (1956). <a href="https://www.degruyter.com/view/books/9781400882618/9781400882618-002/9781400882618-002.xml">"Representation of Events in Nerve Nets and Finite Automata"</a>. <i>Annals of Mathematics Studies</i>. No. 34. Princeton University Press. pp. 3–41. Retrieved 17 June 2017.</cite>
</li>
<li><b><a href="#cite_ref-5">^</a></b> <cite>Hebb, Donald (1949). <a href="https://books.google.com/books?id=ddB4AgAAQBAJ"><i>The Organization of Behavior</i></a>. New York: Wiley. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-135-63190-1"><bdi>978-1-135-63190-1</bdi></a>.</cite>
</li>
<li><b><a href="#cite_ref-6">^</a></b> <cite>Farley, B.G.; W.A. Clark (1954). "Simulation of Self-Organizing Systems by Digital Computer". <i>IRE Transactions on Information Theory</i>. <b>4</b> (4): 76–84. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1109%2FTIT.1954.1057468">10.1109/TIT.1954.1057468</a>.</cite>
</li>
<li><b><a href="#cite_ref-7">^</a></b> Haykin (2008) Neural Networks and Learning Machines, 3rd edition
</li>
<li><b><a href="#cite_ref-8">^</a></b> <cite>Rosenblatt, F. (1958). "The Perceptron: A Probabilistic Model For Information Storage And Organization in the Brain". <i>Psychological Review</i>. <b>65</b> (6): 386–408. <a href="/wiki/CiteSeerX_(identifier)">CiteSeerX</a> <a href="//citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.588.3775">10.1.1.588.3775</a>. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1037%2Fh0042519">10.1037/h0042519</a>. <a href="/wiki/PMID_(identifier)">PMID</a> <a href="//pubmed.ncbi.nlm.nih.gov/13602029">13602029</a>.</cite>
</li>
<li><b><a href="#cite_ref-Werbos_1975_9-0">^</a></b> <cite>Werbos, P.J. (1975). <a href="https://books.google.com/books?id=z81XmgEACAAJ"><i>Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences</i></a>.</cite>
</li>
<li><b><a href="#cite_ref-10">^</a></b> <cite>Rosenblatt, Frank (1957). "The Perceptron—a perceiving and recognizing automaton". <i>Report 85-460-1</i>. Cornell Aeronautical Laboratory.</cite>
</li>
<li><b><a href="#cite_ref-Olazaran_11-0">^</a></b> <cite>Olazaran, Mikel (1996). "A Sociological Study of the Official History of the Perceptrons Controversy". <i>Social Studies of Science</i>. <b>26</b> (3): 611–659. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1177%2F030631296026003005">10.1177/030631296026003005</a>. <a href="/wiki/JSTOR_(identifier)">JSTOR</a> <a href="//www.jstor.org/stable/285702">285702</a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:16786738">16786738</a>.</cite>
</li>
<li>^ <a href="#cite_ref-SCHIDHUB2_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-SCHIDHUB2_12-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-SCHIDHUB2_12-2"><sup><i><b>c</b></i></sup></a> <cite>Schmidhuber, J. (2015). "Deep Learning in Neural Networks: An Overview". <i>Neural Networks</i>. <b>61</b>: 85–117. <a href="/wiki/ArXiv_(identifier)">arXiv</a>:<a href="//arxiv.org/abs/1404.7828">1404.7828</a>. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1016%2Fj.neunet.2014.09.003">10.1016/j.neunet.2014.09.003</a>. <a href="/wiki/PMID_(identifier)">PMID</a> <a href="//pubmed.ncbi.nlm.nih.gov/25462637">25462637</a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:11715509">11715509</a>.</cite>
</li>
<li><b><a href="#cite_ref-ivak1965_13-0">^</a></b> <cite>Ivakhnenko, A. G. (1973). <a href="https://books.google.com/books?id=FhwVNQAACAAJ"><i>Cybernetic Predicting Devices</i></a>. CCM Information Corporation.</cite>
</li>
<li><b><a href="#cite_ref-ivak1967_14-0">^</a></b> <cite>Ivakhnenko, A. G.; Grigorʹevich Lapa, Valentin (1967). <a href="https://books.google.com/books?id=rGFgAAAAMAAJ"><i>Cybernetics and forecasting techniques</i></a>. American Elsevier Pub. Co.</cite>
</li>
<li>^ <a href="#cite_ref-scholarpedia2_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-scholarpedia2_15-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-scholarpedia2_15-2"><sup><i><b>c</b></i></sup></a> <cite><a href="/wiki/J%C3%BCrgen_Schmidhuber">Schmidhuber, Jürgen</a> (2015). <a href="https://doi.org/10.4249%2Fscholarpedia.32832">"Deep Learning"</a>. <i>Scholarpedia</i>. <b>10</b> (11): 85–117. <a href="/wiki/Bibcode_(identifier)">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2015SchpJ..1032832S">2015SchpJ..1032832S</a>. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.4249%2Fscholarpedia.32832">10.4249/scholarpedia.32832</a>.</cite>
</li>
<li><b><a href="#cite_ref-:5_16-0">^</a></b> <cite>Dreyfus, Stuart E. (1 September 1990). "Artificial neural networks, back propagation, and the Kelley-Bryson gradient procedure". <i>Journal of Guidance, Control, and Dynamics</i>. <b>13</b> (5): 926–928. <a href="/wiki/Bibcode_(identifier)">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1990JGCD...13..926D">1990JGCD...13..926D</a>. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2514%2F3.25422">10.2514/3.25422</a>. <a href="/wiki/ISSN_(identifier)">ISSN</a> <a href="//www.worldcat.org/issn/0731-5090">0731-5090</a>.</cite>
</li>
<li><b><a href="#cite_ref-mizutani2000_17-0">^</a></b> <cite>Mizutani, E.; <a href="/wiki/Stuart_Dreyfus">Dreyfus, S.E.</a>; Nishio, K. (2000). "On derivation of MLP backpropagation from the Kelley-Bryson optimal-control gradient formula and its application". <i>Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium</i>. IEEE: 167–172 vol.2. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1109%2Fijcnn.2000.857892">10.1109/ijcnn.2000.857892</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7695-0619-4"><bdi>0-7695-0619-4</bdi></a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:351146">351146</a>.</cite>
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<li><b><a href="#cite_ref-kelley1960_18-0">^</a></b> <cite><a href="/wiki/Henry_J._Kelley">Kelley, Henry J.</a> (1960). "Gradient theory of optimal flight paths". <i>ARS Journal</i>. <b>30</b> (10): 947–954. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2514%2F8.5282">10.2514/8.5282</a>.</cite>
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<li><b><a href="#cite_ref-bryson1961_19-0">^</a></b> <cite>"A gradient method for optimizing multi-stage allocation processes". <i>Proceedings of the Harvard Univ. Symposium on digital computers and their applications</i>. April 1961.</cite>
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<li><b><a href="#cite_ref-20">^</a></b> <cite>Minsky, Marvin; Papert, Seymour (1969). <a href="https://books.google.com/books?id=Ow1OAQAAIAAJ"><i>Perceptrons: An Introduction to Computational Geometry</i></a>. MIT Press. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-63022-1"><bdi>978-0-262-63022-1</bdi></a>.</cite>
</li>
<li><b><a href="#cite_ref-lin1970_21-0">^</a></b> <cite><a href="/wiki/Seppo_Linnainmaa">Linnainmaa, Seppo</a> (1970). <i>The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors</i> (Masters) (in Finnish). University of Helsinki. pp. 6–7.</cite>
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<li><b><a href="#cite_ref-lin1976_22-0">^</a></b> <cite><a href="/wiki/Seppo_Linnainmaa">Linnainmaa, Seppo</a> (1976). "Taylor expansion of the accumulated rounding error". <i>BIT Numerical Mathematics</i>. <b>16</b> (2): 146–160. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2Fbf01931367">10.1007/bf01931367</a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:122357351">122357351</a>.</cite>
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<li><b><a href="#cite_ref-dreyfus1973_23-0">^</a></b> <cite><a href="/wiki/Stuart_Dreyfus">Dreyfus, Stuart</a> (1973). "The computational solution of optimal control problems with time lag". <i>IEEE Transactions on Automatic Control</i>. <b>18</b> (4): 383–385. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1109%2Ftac.1973.1100330">10.1109/tac.1973.1100330</a>.</cite>
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<li><b><a href="#cite_ref-werbos1982_24-0">^</a></b> <cite><a href="/wiki/Paul_Werbos">Werbos, Paul</a> (1982). <a href="http://werbos.com/Neural/SensitivityIFIPSeptember1981.pdf">"Applications of advances in nonlinear sensitivity analysis"</a> (PDF). <i>System modeling and optimization</i>. Springer. pp. 762–770. <a href="https://web.archive.org/web/20160414055503/http://werbos.com/Neural/SensitivityIFIPSeptember1981.pdf">Archived</a> (PDF) from the original on 14 April 2016. Retrieved 2 July 2017.</cite>
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<li><b><a href="#cite_ref-Mead_25-0">^</a></b> <cite><a href="/wiki/Carver_Mead">Mead, Carver A.</a>; Ismail, Mohammed (8 May 1989). <a href="http://fennetic.net/irc/Christopher%20R.%20Carroll%20Carver%20Mead%20Mohammed%20Ismail%20Analog%20VLSI%20Implementation%20of%20Neural%20Systems.pdf"><i>Analog VLSI Implementation of Neural Systems</i></a> (PDF). The Kluwer International Series in Engineering and Computer Science. Vol. 80. Norwell, MA: <a href="/wiki/Kluwer_Academic_Publishers">Kluwer Academic Publishers</a>. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2F978-1-4613-1639-8">10.1007/978-1-4613-1639-8</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4613-1639-8"><bdi>978-1-4613-1639-8</bdi></a>. <a href="https://web.archive.org/web/20191106154442/http://fennetic.net/irc/Christopher%20R.%20Carroll%20Carver%20Mead%20Mohammed%20Ismail%20Analog%20VLSI%20Implementation%20of%20Neural%20Systems.pdf">Archived</a> (PDF) from the original on 6 November 2019. Retrieved 24 January 2020.</cite>
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<li><b><a href="#cite_ref-RUMEL1986_26-0">^</a></b> David E. Rumelhart, Geoffrey E. Hinton &amp; Ronald J. Williams , "<a href="https://www.nature.com/articles/323533a0">Learning representations by back-propagating errors </a> <a href="https://web.archive.org/web/20210308045630/https://www.nature.com/articles/323533a0">Archived</a> 8 March 2021 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a>," <i>Nature', 323, pages 533–536 1986.</i>
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<li><b><a href="#cite_ref-Qian1988_27-0">^</a></b> Qian, Ning, and Terrence J. Sejnowski. "Predicting the secondary structure of globular proteins using neural network models." <i>Journal of molecular biology</i> 202, no. 4 (1988): 865-884.
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<li><b><a href="#cite_ref-Bohr1988_28-0">^</a></b> Bohr, Henrik, Jakob Bohr, Søren Brunak, Rodney MJ Cotterill, Benny Lautrup, Leif Nørskov, Ole H. Olsen, and Steffen B. Petersen. "Protein secondary structure and homology by neural networks The α-helices in rhodopsin." <i>FEBS letters</i> 241, (1988): 223-228
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<li><b><a href="#cite_ref-Rost1993_29-0">^</a></b> Rost, Burkhard, and Chris Sander. "Prediction of protein secondary structure at better than 70% accuracy." <i>Journal of molecular biology</i> 232, no. 2 (1993): 584-599.
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<li><b><a href="#cite_ref-Weng1992_30-0">^</a></b> J. Weng, N. Ahuja and T. S. Huang, "<a href="http://www.cse.msu.edu/~weng/research/CresceptronIJCNN1992.pdf">Cresceptron: a self-organizing neural network which grows adaptively</a> <a href="https://web.archive.org/web/20170921205838/http://www.cse.msu.edu/%7Eweng/research/CresceptronIJCNN1992.pdf">Archived</a> 21 September 2017 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a>," <i>Proc. International Joint Conference on Neural Networks</i>, Baltimore, Maryland, vol I, pp. 576–581, June 1992.
</li>
<li><b><a href="#cite_ref-Weng19932_31-0">^</a></b> J. Weng, N. Ahuja and T. S. Huang, "<a href="http://www.cse.msu.edu/~weng/research/CresceptronICCV1993.pdf">Learning recognition and segmentation of 3-D objects from 2-D images</a> <a href="https://web.archive.org/web/20170921203756/http://www.cse.msu.edu/%7Eweng/research/CresceptronICCV1993.pdf">Archived</a> 21 September 2017 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a>," <i>Proc. 4th International Conf. Computer Vision</i>, Berlin, Germany, pp. 121–128, May 1993.
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<li><b><a href="#cite_ref-Weng1997_32-0">^</a></b> J. Weng, N. Ahuja and T. S. Huang, "<a href="http://www.cse.msu.edu/~weng/research/CresceptronIJCV.pdf">Learning recognition and segmentation using the Cresceptron</a> <a href="https://web.archive.org/web/20210125215527/http://www.cse.msu.edu/~weng/research/CresceptronIJCV.pdf">Archived</a> 25 January 2021 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a>," <i>International Journal of Computer Vision</i>, vol. 25, no. 2, pp. 105–139, Nov. 1997.
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<li><b><a href="#cite_ref-SCHMID1992_33-0">^</a></b> J. Schmidhuber., "<a href="https://mediatum.ub.tum.de/doc/814767/file.pdf">Learning complex, extended sequences using the principle of history compression</a> <a href="https://web.archive.org/web/20200318023723/https://mediatum.ub.tum.de/doc/814767/file.pdf">Archived</a> 18 March 2020 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a>," <i>Neural Computation</i>, 4, pp. 234–242, 1992.
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<li><b><a href="#cite_ref-35">^</a></b> <cite><a href="/wiki/Pedro_Domingos">Domingos, Pedro</a> (22 September 2015). "chapter 4". <i>The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World</i>. <a href="/wiki/Basic_Books">Basic Books</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0465065707"><bdi>978-0465065707</bdi></a>.</cite>
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<li><b><a href="#cite_ref-smolensky1986_36-0">^</a></b> <cite><a href="/wiki/Paul_Smolensky">Smolensky, P.</a> (1986). <a href="http://portal.acm.org/citation.cfm?id=104290">"Information processing in dynamical systems: Foundations of harmony theory."</a>. In D. E. Rumelhart; J. L. McClelland; PDP Research Group (eds.). <a href="https://archive.org/details/paralleldistribu00rume/page/194"><i>Parallel Distributed Processing: Explorations in the Microstructure of Cognition</i></a>. Vol. 1. pp. <a href="https://archive.org/details/paralleldistribu00rume/page/194">194–281</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-68053-0"><bdi>978-0-262-68053-0</bdi></a>.</cite>
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<li><b><a href="#cite_ref-ng2012_37-0">^</a></b> <cite>Ng, Andrew; Dean, Jeff (2012). "Building High-level Features Using Large Scale Unsupervised Learning". <a href="/wiki/ArXiv_(identifier)">arXiv</a>:<a href="//arxiv.org/abs/1112.6209">1112.6209</a> [<a href="//arxiv.org/archive/cs.LG">cs.LG</a>].</cite>
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<li><b><a href="#cite_ref-38">^</a></b> <cite>Ian Goodfellow and Yoshua Bengio and Aaron Courville (2016). <a href="http://www.deeplearningbook.org/"><i>Deep Learning</i></a>. MIT Press. <a href="https://web.archive.org/web/20160416111010/http://www.deeplearningbook.org/">Archived</a> from the original on 16 April 2016. Retrieved 1 June 2016.</cite>
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<li><b><a href="#cite_ref-:3_39-0">^</a></b> <cite>Cireşan, Dan Claudiu; Meier, Ueli; Gambardella, Luca Maria; Schmidhuber, Jürgen (21 September 2010). "Deep, Big, Simple Neural Nets for Handwritten Digit Recognition". <i>Neural Computation</i>. <b>22</b> (12): 3207–3220. <a href="/wiki/ArXiv_(identifier)">arXiv</a>:<a href="//arxiv.org/abs/1003.0358">1003.0358</a>. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1162%2Fneco_a_00052">10.1162/neco_a_00052</a>. <a href="/wiki/ISSN_(identifier)">ISSN</a> <a href="//www.worldcat.org/issn/0899-7667">0899-7667</a>. <a href="/wiki/PMID_(identifier)">PMID</a> <a href="//pubmed.ncbi.nlm.nih.gov/20858131">20858131</a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:1918673">1918673</a>.</cite>
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<li><b><a href="#cite_ref-Scherer2010_40-0">^</a></b> Dominik Scherer, Andreas C. Müller, and Sven Behnke: "<a href="https://www.ais.uni-bonn.de/papers/icann2010_maxpool.pdf">Evaluation of Pooling Operations in Convolutional Architectures for Object Recognition</a> <a href="https://web.archive.org/web/20180403185041/http://ais.uni-bonn.de/papers/icann2010_maxpool.pdf">Archived</a> 3 April 2018 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a>," <i>In 20th International Conference Artificial Neural Networks (ICANN)</i>, pp. 92–101, 2010. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2F978-3-642-15825-4_10">10.1007/978-3-642-15825-4_10</a>.
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<li><b><a href="#cite_ref-143">^</a></b> <cite>Xu, Zhiqin John; Zhou, Hanxu (18 May 2021). <a href="https://ojs.aaai.org/index.php/AAAI/article/view/17261">"Deep Frequency Principle Towards Understanding Why Deeper Learning Is Faster"</a>. <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>. <b>35</b> (12): 10541–10550. <a href="/wiki/ArXiv_(identifier)">arXiv</a>:<a href="//arxiv.org/abs/2007.14313">2007.14313</a>. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1609%2Faaai.v35i12.17261">10.1609/aaai.v35i12.17261</a>. <a href="/wiki/ISSN_(identifier)">ISSN</a> <a href="//www.worldcat.org/issn/2374-3468">2374-3468</a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:220831156">220831156</a>. <a href="https://web.archive.org/web/20211005142300/https://ojs.aaai.org/index.php/AAAI/article/view/17261">Archived</a> from the original on 5 October 2021. Retrieved 5 October 2021.</cite>
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<li><b><a href="#cite_ref-144">^</a></b> <cite>Dewdney, A. K. (1 April 1997). <a href="https://books.google.com/books?id=KcHaAAAAMAAJ&amp;pg=PA82"><i>Yes, we have no neutrons: an eye-opening tour through the twists and turns of bad science</i></a>. Wiley. p. 82. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-10806-1"><bdi>978-0-471-10806-1</bdi></a>.</cite>
</li>
<li><b><a href="#cite_ref-145">^</a></b> <a href="http://www.nasa.gov/centers/dryden/news/NewsReleases/2003/03-49.html">NASA – Dryden Flight Research Center – News Room: News Releases: NASA NEURAL NETWORK PROJECT PASSES MILESTONE</a> <a href="https://web.archive.org/web/20100402065100/http://www.nasa.gov/centers/dryden/news/NewsReleases/2003/03-49.html">Archived</a> 2 April 2010 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a>. Nasa.gov. Retrieved on 20 November 2013.
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<li><b><a href="#cite_ref-146">^</a></b> <cite><a href="https://web.archive.org/web/20120319163352/http://members.fortunecity.com/templarseries/popper.html">"Roger Bridgman's defence of neural networks"</a>. Archived from <a href="http://members.fortunecity.com/templarseries/popper.html">the original</a> on 19 March 2012. Retrieved 12 July 2010.</cite>
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<li><b><a href="#cite_ref-VanEssen1991_147-0">^</a></b> D. J. Felleman and D. C. Van Essen, "<a href="https://archive.today/20150120022056/http://cercor.oxfordjournals.org/content/1/1/1.1.full.pdf+html">Distributed hierarchical processing in the primate cerebral cortex</a>," <i>Cerebral Cortex</i>, 1, pp. 1–47, 1991.
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<li><b><a href="#cite_ref-Weng2012_148-0">^</a></b> J. Weng, "<a href="https://www.amazon.com/Natural-Artificial-Intelligence-Introduction-Computational/dp/0985875720">Natural and Artificial Intelligence: Introduction to Computational Brain-Mind</a>," BMI Press, <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-9858757-2-5">978-0-9858757-2-5</a>, 2012.
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<li>^ <a href="#cite_ref-:0_149-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_149-1"><sup><i><b>b</b></i></sup></a> <cite>Edwards, Chris (25 June 2015). "Growing pains for deep learning". <i>Communications of the ACM</i>. <b>58</b> (7): 14–16. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1145%2F2771283">10.1145/2771283</a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:11026540">11026540</a>.</cite>
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<li><b><a href="#cite_ref-150">^</a></b> <cite>Cade Metz (18 May 2016). <a href="https://www.wired.com/2016/05/google-tpu-custom-chips/">"Google Built Its Very Own Chips to Power Its AI Bots"</a>. <i>Wired</i>. <a href="https://web.archive.org/web/20180113150305/https://www.wired.com/2016/05/google-tpu-custom-chips/">Archived</a> from the original on 13 January 2018. Retrieved 5 March 2017.</cite>
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<li><b><a href="#cite_ref-151">^</a></b> <cite><a href="http://yann.lecun.com/exdb/publis/pdf/bengio-lecun-07.pdf">"Scaling Learning Algorithms towards AI"</a> (PDF). <a href="https://web.archive.org/web/20220812081157/http://yann.lecun.com/exdb/publis/pdf/bengio-lecun-07.pdf">Archived</a> (PDF) from the original on 12 August 2022. Retrieved 6 July 2022.</cite>
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<li><b><a href="#cite_ref-152">^</a></b> <cite>Tahmasebi; Hezarkhani (2012). <a href="//www.ncbi.nlm.nih.gov/pmc/articles/PMC4268588">"A hybrid neural networks-fuzzy logic-genetic algorithm for grade estimation"</a>. <i>Computers &amp; Geosciences</i>. <b>42</b>: 18–27. <a href="/wiki/Bibcode_(identifier)">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2012CG.....42...18T">2012CG.....42...18T</a>. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1016%2Fj.cageo.2012.02.004">10.1016/j.cageo.2012.02.004</a>. <a href="/wiki/PMC_(identifier)">PMC</a> <a href="//www.ncbi.nlm.nih.gov/pmc/articles/PMC4268588">4268588</a>. <a href="/wiki/PMID_(identifier)">PMID</a> <a href="//pubmed.ncbi.nlm.nih.gov/25540468">25540468</a>.</cite>
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</ol></div>
<h2>Bibliography[<a href="/w/index.php?title=Artificial_neural_network&amp;action=edit&amp;section=39">edit</a>]</h2>
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<ul><li><cite>Bhadeshia H. K. D. H. (1999). <a href="http://www.msm.cam.ac.uk/phase-trans/abstracts/neural.review.pdf">"Neural Networks in Materials Science"</a> (PDF). <i>ISIJ International</i>. <b>39</b> (10): 966–979. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.2355%2Fisijinternational.39.966">10.2355/isijinternational.39.966</a>.</cite></li>
<li><cite>Bishop, Christopher M. (1995). <i>Neural networks for pattern recognition</i>. Clarendon Press. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-853849-3"><bdi>978-0-19-853849-3</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/33101074">33101074</a>.</cite></li>
<li><cite>Borgelt, Christian (2003). <i>Neuro-Fuzzy-Systeme : von den Grundlagen künstlicher Neuronaler Netze zur Kopplung mit Fuzzy-Systemen</i>. Vieweg. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-528-25265-6"><bdi>978-3-528-25265-6</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/76538146">76538146</a>.</cite></li>
<li><cite><a href="/wiki/George_Cybenko">Cybenko, G.V.</a> (2006). <a href="https://books.google.com/books?id=4RtVAAAAMAAJ&amp;pg=PA303">"Approximation by Superpositions of a Sigmoidal function"</a>. In van Schuppen, Jan H. (ed.). <a href="/wiki/Mathematics_of_Control,_Signals,_and_Systems"><i>Mathematics of Control, Signals, and Systems</i></a>. Springer International. pp. 303–314.</cite> <a href="https://web.archive.org/web/20110719183058/http://actcomm.dartmouth.edu/gvc/papers/approx_by_superposition.pdf">PDF</a></li>
<li><cite>Dewdney, A. K. (1997). <i>Yes, we have no neutrons : an eye-opening tour through the twists and turns of bad science</i>. New York: Wiley. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-10806-1"><bdi>978-0-471-10806-1</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/35558945">35558945</a>.</cite></li>
<li><cite>Duda, Richard O.; Hart, Peter Elliot; Stork, David G. (2001). <i>Pattern classification</i> (2 ed.). Wiley. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-05669-0"><bdi>978-0-471-05669-0</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/41347061">41347061</a>.</cite></li>
<li><cite>Egmont-Petersen, M.; de Ridder, D.; Handels, H. (2002). "Image processing with neural networks – a review". <i>Pattern Recognition</i>. <b>35</b> (10): 2279–2301. <a href="/wiki/CiteSeerX_(identifier)">CiteSeerX</a> <a href="//citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.5444">10.1.1.21.5444</a>. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1016%2FS0031-3203%2801%2900178-9">10.1016/S0031-3203(01)00178-9</a>.</cite></li>
<li><cite>Fahlman, S.; Lebiere, C (1991). <a href="https://web.archive.org/web/20130503184045/http://www.cs.iastate.edu/~honavar/fahlman.pdf">"The Cascade-Correlation Learning Architecture"</a> (PDF). Archived from <a href="http://www.cs.iastate.edu/~honavar/fahlman.pdf">the original</a> (PDF) on 3 May 2013. Retrieved 28 August 2006.</cite>
<ul><li>created for <a href="/wiki/National_Science_Foundation">National Science Foundation</a>, Contract Number EET-8716324, and <a href="/wiki/Defense_Advanced_Research_Projects_Agency">Defense Advanced Research Projects Agency</a> (DOD), ARPA Order No. 4976 under Contract F33615-87-C-1499.</li></ul></li>
<li><cite>Gurney, Kevin (1997). <i>An introduction to neural networks</i>. UCL Press. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-85728-673-1"><bdi>978-1-85728-673-1</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/37875698">37875698</a>.</cite></li>
<li><cite>Haykin, Simon S. (1999). <i>Neural networks : a comprehensive foundation</i>. Prentice Hall. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-273350-2"><bdi>978-0-13-273350-2</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/38908586">38908586</a>.</cite></li>
<li><cite>Hertz, J.; Palmer, Richard G.; Krogh, Anders S. (1991). <i>Introduction to the theory of neural computation</i>. Addison-Wesley. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-51560-2"><bdi>978-0-201-51560-2</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/21522159">21522159</a>.</cite></li>
<li><cite><i>Information theory, inference, and learning algorithms</i>. Cambridge University Press. 25 September 2003. <a href="/wiki/Bibcode_(identifier)">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2003itil.book.....M">2003itil.book.....M</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-64298-9"><bdi>978-0-521-64298-9</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/52377690">52377690</a>.</cite></li>
<li><cite>Kruse, Rudolf; Borgelt, Christian; Klawonn, F.; Moewes, Christian; Steinbrecher, Matthias; Held, Pascal (2013). <i>Computational intelligence : a methodological introduction</i>. Springer. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4471-5012-1"><bdi>978-1-4471-5012-1</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/837524179">837524179</a>.</cite></li>
<li><cite>Lawrence, Jeanette (1994). <i>Introduction to neural networks : design, theory and applications</i>. California Scientific Software. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-883157-00-5"><bdi>978-1-883157-00-5</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/32179420">32179420</a>.</cite></li>
<li><cite><a href="/wiki/David_J.C._MacKay">MacKay, David, J.C.</a> (2003). <a href="http://www.inference.phy.cam.ac.uk/itprnn/book.pdf"><i>Information Theory, Inference, and Learning Algorithms</i></a> (PDF). <a href="/wiki/Cambridge_University_Press">Cambridge University Press</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-64298-9"><bdi>978-0-521-64298-9</bdi></a>.</cite></li>
<li><cite>Masters, Timothy (1994). <i>Signal and image processing with neural networks : a C++ sourcebook</i>. J. Wiley. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-04963-0"><bdi>978-0-471-04963-0</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/29877717">29877717</a>.</cite></li>
<li><cite>Maurer, Harald (2021). <i>Cognitive science : integrative synchronization mechanisms in cognitive neuroarchitectures of the modern connectionism</i>. CRC Press. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1201%2F9781351043526">10.1201/9781351043526</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-351-04352-6"><bdi>978-1-351-04352-6</bdi></a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:242963768">242963768</a>.</cite></li>
<li><cite><a href="/wiki/Brian_D._Ripley">Ripley, Brian D.</a> (2007). <a href="https://books.google.com/books?id=m12UR8QmLqoC"><i>Pattern Recognition and Neural Networks</i></a>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-71770-0"><bdi>978-0-521-71770-0</bdi></a>.</cite></li>
<li><cite>Siegelmann, H.T.; Sontag, Eduardo D. (1994). "Analog computation via neural networks". <i>Theoretical Computer Science</i>. <b>131</b> (2): 331–360. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1016%2F0304-3975%2894%2990178-3">10.1016/0304-3975(94)90178-3</a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:2456483">2456483</a>.</cite></li>
<li><cite>Smith, Murray (1993). <i>Neural networks for statistical modeling</i>. Van Nostrand Reinhold. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-442-01310-3"><bdi>978-0-442-01310-3</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/27145760">27145760</a>.</cite></li>
<li><cite>Wasserman, Philip D. (1993). <i>Advanced methods in neural computing</i>. Van Nostrand Reinhold. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-442-00461-3"><bdi>978-0-442-00461-3</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/27429729">27429729</a>.</cite></li>
<li><cite>Wilson, Halsey (2018). <i>Artificial intelligence</i>. Grey House Publishing. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-68217-867-6"><bdi>978-1-68217-867-6</bdi></a>.</cite></li></ul>
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 * 1 Training
 * 2 History
 * 3 Models
 + 3.1 Artificial neurons
 + 3.2 Organization
 + 3.3 Hyperparameter
 + 3.4 Learning
 o 3.4.1 Learning rate
 o 3.4.2 Cost function
 o 3.4.3 Backpropagation
 + 3.5 Learning paradigms
 o 3.5.1 Supervised learning
 o 3.5.2 Unsupervised learning
 o 3.5.3 Reinforcement learning
 o 3.5.4 Self-learning
 o 3.5.5 Neuroevolution
 + 3.6 Stochastic neural network
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 o 3.7.1 Modes
 * 4 Types
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 Part of a series on 
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 An artificial neural network is an interconnected group of nodes, inspired by a simplification of neurons in a brain. Here, each circular node represents an artificial neuron and an arrow represents a connection from the output of one artificial neuron to the input of another.

 Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets,[1] are computing systems inspired by the biological neural networks that constitute animal brains.[2]

 An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons. An artificial neuron receives signals then processes them and can signal neurons connected to it. The "signal" at a connection is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs. The connections are called edges. Neurons and edges typically have a weight that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Neurons may have a threshold such that a signal is sent only if the aggregate signal crosses that threshold.

 Typically, neurons are aggregated into layers. Different layers may perform different transformations on their inputs. Signals travel from the first layer (the input layer), to the last layer (the output layer), possibly after traversing the layers multiple times.

 Training [ edit ]

 Neural networks learn (or are trained) by processing examples, each of which contains a known "input" and "result," forming probability-weighted associations between the two, which are stored within the data structure of the net itself. The training of a neural network from a given example is usually conducted by determining the difference between the processed output of the network (often a prediction) and a target output. This difference is the error. The network then adjusts its weighted associations according to a learning rule and using this error value. Successive adjustments will cause the neural network to produce output that is increasingly similar to the target output. After a sufficient number of these adjustments, the training can be terminated based on certain criteria. This is known as supervised learning.

 Such systems "learn" to perform tasks by considering examples, generally without being programmed with task-specific rules. For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as "cat" or "no cat" and using the results to identify cats in other images. They do this without any prior knowledge of cats, for example, that they have fur, tails, whiskers, and cat-like faces. Instead, they automatically generate identifying characteristics from the examples that they process.

 History [ edit ]

 Main article: History of artificial neural networks

 Warren McCulloch and Walter Pitts[3] (1943) opened the subject by creating a computational model for neural networks.[4] In the late 1940s, D. O. Hebb[5] created a learning hypothesis based on the mechanism of neural plasticity that became known as Hebbian learning. Farley and Wesley A. Clark[6] (1954) first used computational machines, then called "calculators", to simulate a Hebbian network. In 1958, psychologist Frank Rosenblatt invented the perceptron, the first artificial neural network,[7][8][9][10] funded by the United States Office of Naval Research.[11] The first functional networks with many layers were published by Ivakhnenko and Lapa in 1965, as the Group Method of Data Handling.[12][13][14] The basics of continuous backpropagation[12][15][16][17] were derived in the context of control theory by Kelley[18] in 1960 and by Bryson in 1961,[19] using principles of dynamic programming. Thereafter research stagnated following Minsky and Papert (1969),[20] who discovered that basic perceptrons were incapable of processing the exclusive-or circuit and that computers lacked sufficient power to process useful neural networks.

 In 1970, Seppo Linnainmaa published the general method for automatic differentiation (AD) of discrete connected networks of nested differentiable functions.[21][22] In 1973, Dreyfus used backpropagation to adapt parameters of controllers in proportion to error gradients.[23] Werbos's (1975) backpropagation algorithm enabled practical training of multi-layer networks. In 1982, he applied Linnainmaa's AD method to neural networks in the way that became widely used.[15][24]

 The development of metal–oxide–semiconductor (MOS) very-large-scale integration (VLSI), in the form of complementary MOS (CMOS) technology, enabled increasing MOS transistor counts in digital electronics. This provided more processing power for the development of practical artificial neural networks in the 1980s.[25]

 In 1986 Rumelhart, Hinton and Williams showed that backpropagation learned interesting internal representations of words as feature vectors when trained to predict the next word in a sequence.[26]

 From 1988 onward,[27][28] the use of neural networks transformed the field of protein structure prediction, in particular when the first cascading networks were trained on profiles (matrices) produced by multiple sequence alignments.[29]

 In 1992, max-pooling was introduced to help with least-shift invariance and tolerance to deformation to aid 3D object recognition.[30][31][32] Schmidhuber adopted a multi-level hierarchy of networks (1992) pre-trained one level at a time by unsupervised learning and fine-tuned by backpropagation.[33]

 Neural networks' early successes included predicting the stock market and in 1995 a (mostly) self-driving car.[a][34]

 Geoffrey Hinton et al. (2006) proposed learning a high-level representation using successive layers of binary or real-valued latent variables with a restricted Boltzmann machine[35] to model each layer. In 2012, Ng and Dean created a network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images.[36] Unsupervised pre-training and increased computing power from GPUs and distributed computing allowed the use of larger networks, particularly in image and visual recognition problems, which became known as "deep learning".[37]

 Ciresan and colleagues (2010)[38] showed that despite the vanishing gradient problem, GPUs make backpropagation feasible for many-layered feedforward neural networks.[39] Between 2009 and 2012, ANNs began winning prizes in image recognition contests, approaching human level performance on various tasks, initially in pattern recognition and handwriting recognition.[40][41] For example, the bi-directional and multi-dimensional long short-term memory (LSTM)[42][43] of Graves et al. won three competitions in connected handwriting recognition in 2009 without any prior knowledge about the three languages to be learned.[42][43]

 Ciresan and colleagues built the first pattern recognizers to achieve human-competitive/superhuman performance[44] on benchmarks such as traffic sign recognition (IJCNN 2012).

 Models [ edit ]

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 Further information: Mathematics of artificial neural networks
 Neuron and myelinated axon, with signal flow from inputs at dendrites to outputs at axon terminals

 ANNs began as an attempt to exploit the architecture of the human brain to perform tasks that conventional algorithms had little success with. They soon reoriented towards improving empirical results, mostly abandoning attempts to remain true to their biological precursors. Neurons are connected to each other in various patterns, to allow the output of some neurons to become the input of others. The network forms a directed, weighted graph.[45]

 An artificial neural network consists of a collection of simulated neurons. Each neuron is a node which is connected to other nodes via links that correspond to biological axon-synapse-dendrite connections. Each link has a weight, which determines the strength of one node's influence on another.[46]

 Artificial neurons [ edit ]

 ANNs are composed of artificial neurons which are conceptually derived from biological neurons. Each artificial neuron has inputs and produces a single output which can be sent to multiple other neurons.[47] The inputs can be the feature values of a sample of external data, such as images or documents, or they can be the outputs of other neurons. The outputs of the final output neurons of the neural net accomplish the task, such as recognizing an object in an image.

 To find the output of the neuron we take the weighted sum of all the inputs, weighted by the weights of the connections from the inputs to the neuron. We add a bias term to this sum.[48] This weighted sum is sometimes called the activation. This weighted sum is then passed through a (usually nonlinear) activation function to produce the output. The initial inputs are external data, such as images and documents. The ultimate outputs accomplish the task, such as recognizing an object in an image.[49]

 Organization [ edit ]

 The neurons are typically organized into multiple layers, especially in deep learning. Neurons of one layer connect only to neurons of the immediately preceding and immediately following layers. The layer that receives external data is the input layer. The layer that produces the ultimate result is the output layer. In between them are zero or more hidden layers. Single layer and unlayered networks are also used. Between two layers, multiple connection patterns are possible. They can be 'fully connected', with every neuron in one layer connecting to every neuron in the next layer. They can be pooling, where a group of neurons in one layer connect to a single neuron in the next layer, thereby reducing the number of neurons in that layer.[50] Neurons with only such connections form a directed acyclic graph and are known as feedforward networks.[51] Alternatively, networks that allow connections between neurons in the same or previous layers are known as recurrent networks.[52]

 Hyperparameter [ edit ]

 Main article: Hyperparameter (machine learning)

 A hyperparameter is a constant parameter whose value is set before the learning process begins. The values of parameters are derived via learning. Examples of hyperparameters include learning rate, the number of hidden layers and batch size.[53] The values of some hyperparameters can be dependent on those of other hyperparameters. For example, the size of some layers can depend on the overall number of layers.

 Learning [ edit ]

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 See also: Mathematical optimization, Estimation theory, and Machine learning

 Learning is the adaptation of the network to better handle a task by considering sample observations. Learning involves adjusting the weights (and optional thresholds) of the network to improve the accuracy of the result. This is done by minimizing the observed errors. Learning is complete when examining additional observations does not usefully reduce the error rate. Even after learning, the error rate typically does not reach 0. If after learning, the error rate is too high, the network typically must be redesigned. Practically this is done by defining a cost function that is evaluated periodically during learning. As long as its output continues to decline, learning continues. The cost is frequently defined as a statistic whose value can only be approximated. The outputs are actually numbers, so when the error is low, the difference between the output (almost certainly a cat) and the correct answer (cat) is small. Learning attempts to reduce the total of the differences across the observations. Most learning models can be viewed as a straightforward application of optimization theory and statistical estimation.[45][54]

 Learning rate [ edit ]

 The learning rate defines the size of the corrective steps that the model takes to adjust for errors in each observation.[55] A high learning rate shortens the training time, but with lower ultimate accuracy, while a lower learning rate takes longer, but with the potential for greater accuracy. Optimizations such as Quickprop are primarily aimed at speeding up error minimization, while other improvements mainly try to increase reliability. In order to avoid oscillation inside the network such as alternating connection weights, and to improve the rate of convergence, refinements use an adaptive learning rate that increases or decreases as appropriate.[56] The concept of momentum allows the balance between the gradient and the previous change to be weighted such that the weight adjustment depends to some degree on the previous change. A momentum close to 0 emphasizes the gradient, while a value close to 1 emphasizes the last change.

 Cost function [ edit ]

 While it is possible to define a cost function ad hoc, frequently the choice is determined by the function's desirable properties (such as convexity) or because it arises from the model (e.g. in a probabilistic model the model's posterior probability can be used as an inverse cost).

 Backpropagation [ edit ]

 Main article: Backpropagation

 Backpropagation is a method used to adjust the connection weights to compensate for each error found during learning. The error amount is effectively divided among the connections. Technically, backprop calculates the gradient (the derivative) of the cost function associated with a given state with respect to the weights. The weight updates can be done via stochastic gradient descent or other methods, such as Extreme Learning Machines,[57] "No-prop" networks,[58] training without backtracking,[59] "weightless" networks,[60][61] and non-connectionist neural networks.[ citation needed ]

 Learning paradigms [ edit ]

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 Machine learning is commonly separated into three main learning paradigms, supervised learning, unsupervised learning and reinforcement learning.[62] Each corresponds to a particular learning task.

 Supervised learning [ edit ]

 Supervised learning uses a set of paired inputs and desired outputs. The learning task is to produce the desired output for each input. In this case, the cost function is related to eliminating incorrect deductions.[63] A commonly used cost is the mean-squared error, which tries to minimize the average squared error between the network's output and the desired output. Tasks suited for supervised learning are pattern recognition (also known as classification) and regression (also known as function approximation). Supervised learning is also applicable to sequential data (e.g., for hand writing, speech and gesture recognition). This can be thought of as learning with a "teacher", in the form of a function that provides continuous feedback on the quality of solutions obtained thus far.

 Unsupervised learning [ edit ]

 In unsupervised learning, input data is given along with the cost function, some function of the data and the network's output. The cost function is dependent on the task (the model domain) and any a priori assumptions (the implicit properties of the model, its parameters and the observed variables). As a trivial example, consider the model where is a constant and the cost . Minimizing this cost produces a value of that is equal to the mean of the data. The cost function can be much more complicated. Its form depends on the application: for example, in compression it could be related to the mutual information between and , whereas in statistical modeling, it could be related to the posterior probability of the model given the data (note that in both of those examples, those quantities would be maximized rather than minimized). Tasks that fall within the paradigm of unsupervised learning are in general estimation problems; the applications include clustering, the estimation of statistical distributions, compression and filtering.

 Reinforcement learning [ edit ]

 Main article: Reinforcement learning
 See also: Stochastic control

 In applications such as playing video games, an actor takes a string of actions, receiving a generally unpredictable response from the environment after each one. The goal is to win the game, i.e., generate the most positive (lowest cost) responses. In reinforcement learning, the aim is to weight the network (devise a policy) to perform actions that minimize long-term (expected cumulative) cost. At each point in time the agent performs an action and the environment generates an observation and an instantaneous cost, according to some (usually unknown) rules. The rules and the long-term cost usually only can be estimated. At any juncture, the agent decides whether to explore new actions to uncover their costs or to exploit prior learning to proceed more quickly.

 Formally the environment is modeled as a Markov decision process (MDP) with states and actions . Because the state transitions are not known, probability distributions are used instead: the instantaneous cost distribution , the observation distribution and the transition distribution , while a policy is defined as the conditional distribution over actions given the observations. Taken together, the two define a Markov chain (MC). The aim is to discover the lowest-cost MC.

 ANNs serve as the learning component in such applications.[64][65] Dynamic programming coupled with ANNs (giving neurodynamic programming)[66] has been applied to problems such as those involved in vehicle routing,[67] video games, natural resource management[68][69] and medicine[70] because of ANNs ability to mitigate losses of accuracy even when reducing the discretization grid density for numerically approximating the solution of control problems. Tasks that fall within the paradigm of reinforcement learning are control problems, games and other sequential decision making tasks.

 Self-learning [ edit ]

 Self-learning in neural networks was introduced in 1982 along with a neural network capable of self-learning named Crossbar Adaptive Array (CAA).[71] It is a system with only one input, situation s, and only one output, action (or behavior) a. It has neither external advice input nor external reinforcement input from the environment. The CAA computes, in a crossbar fashion, both decisions about actions and emotions (feelings) about encountered situations. The system is driven by the interaction between cognition and emotion.[72] Given the memory matrix, W =||w(a,s)||, the crossbar self-learning algorithm in each iteration performs the following computation:

 In situation s perform action a;
 Receive consequence situation s';
 Compute emotion of being in consequence situation v(s');
 Update crossbar memory w'(a,s) = w(a,s) + v(s').
 

 The backpropagated value (secondary reinforcement) is the emotion toward the consequence situation. The CAA exists in two environments, one is behavioral environment where it behaves, and the other is genetic environment, where from it initially and only once receives initial emotions about to be encountered situations in the behavioral environment. Having received the genome vector (species vector) from the genetic environment, the CAA will learn a goal-seeking behavior, in the behavioral environment that contains both desirable and undesirable situations.[73]

 Neuroevolution [ edit ]

 Main article: Neuroevolution

 Neuroevolution can create neural network topologies and weights using evolutionary computation. It is competitive with sophisticated gradient descent approaches[ citation needed ]. One advantage of neuroevolution is that it may be less prone to get caught in "dead ends".[74]

 Stochastic neural network [ edit ]

 Stochastic neural networks originating from Sherrington–Kirkpatrick models are a type of artificial neural network built by introducing random variations into the network, either by giving the network's artificial neurons stochastic transfer functions, or by giving them stochastic weights. This makes them useful tools for optimization problems, since the random fluctuations help the network escape from local minima.[75] Stochastic neural networks trained using a Bayesian approach are known as Bayesian neural networks.[76]

 Other [ edit ]

 In a Bayesian framework, a distribution over the set of allowed models is chosen to minimize the cost. Evolutionary methods,[77] gene expression programming,[78] simulated annealing,[79] expectation-maximization, non-parametric methods and particle swarm optimization[80] are other learning algorithms. Convergent recursion is a learning algorithm for cerebellar model articulation controller (CMAC) neural networks.[81][82]

 Modes [ edit ]

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 Two modes of learning are available: stochastic and batch. In stochastic learning, each input creates a weight adjustment. In batch learning weights are adjusted based on a batch of inputs, accumulating errors over the batch. Stochastic learning introduces "noise" into the process, using the local gradient calculated from one data point; this reduces the chance of the network getting stuck in local minima. However, batch learning typically yields a faster, more stable descent to a local minimum, since each update is performed in the direction of the batch's average error. A common compromise is to use "mini-batches", small batches with samples in each batch selected stochastically from the entire data set.

 Types [ edit ]

 Main article: Types of artificial neural networks

 ANNs have evolved into a broad family of techniques that have advanced the state of the art across multiple domains. The simplest types have one or more static components, including number of units, number of layers, unit weights and topology. Dynamic types allow one or more of these to evolve via learning. The latter are much more complicated, but can shorten learning periods and produce better results. Some types allow/require learning to be "supervised" by the operator, while others operate independently. Some types operate purely in hardware, while others are purely software and run on general purpose computers.

 Some of the main breakthroughs include: convolutional neural networks that have proven particularly successful in processing visual and other two-dimensional data;[83][84] long short-term memory avoid the vanishing gradient problem[85] and can handle signals that have a mix of low and high frequency components aiding large-vocabulary speech recognition,[86][87] text-to-speech synthesis,[88][15][89] and photo-real talking heads;[90] competitive networks such as generative adversarial networks in which multiple networks (of varying structure) compete with each other, on tasks such as winning a game[91] or on deceiving the opponent about the authenticity of an input.[92]

 Network design [ edit ]

 Main article: Neural architecture search

 Neural architecture search (NAS) uses machine learning to automate ANN design. Various approaches to NAS have designed networks that compare well with hand-designed systems. The basic search algorithm is to propose a candidate model, evaluate it against a dataset and use the results as feedback to teach the NAS network.[93] Available systems include AutoML and AutoKeras.[94]

 Design issues include deciding the number, type and connectedness of network layers, as well as the size of each and the connection type (full, pooling, ...).

 Hyperparameters must also be defined as part of the design (they are not learned), governing matters such as how many neurons are in each layer, learning rate, step, stride, depth, receptive field and padding (for CNNs), etc.[95]

 Use [ edit ]

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 Using Artificial neural networks requires an understanding of their characteristics.

 * Choice of model: This depends on the data representation and the application. Overly complex models are slow learning.
 * Learning algorithm: Numerous trade-offs exist between learning algorithms. Almost any algorithm will work well with the correct hyperparameters for training on a particular data set. However, selecting and tuning an algorithm for training on unseen data requires significant experimentation.
 * Robustness: If the model, cost function and learning algorithm are selected appropriately, the resulting ANN can become robust.

 ANN capabilities fall within the following broad categories:[ citation needed ]

 * Function approximation, or regression analysis, including time series prediction, fitness approximation and modeling.
 * Classification, including pattern and sequence recognition, novelty detection and sequential decision making.[96]
 * Data processing, including filtering, clustering, blind source separation and compression.
 * Robotics, including directing manipulators and prostheses.

 Applications [ edit ]

 Because of their ability to reproduce and model nonlinear processes, artificial neural networks have found applications in many disciplines. Application areas include system identification and control (vehicle control, trajectory prediction,[97] process control, natural resource management), quantum chemistry,[98] general game playing,[99] pattern recognition (radar systems, face identification, signal classification,[100] 3D reconstruction,[101] object recognition and more), sensor data analysis,[102] sequence recognition (gesture, speech, handwritten and printed text recognition[103]), medical diagnosis, finance[104] (e.g. automated trading systems), data mining, visualization, machine translation, social network filtering[105] and e-mail spam filtering. ANNs have been used to diagnose several types of cancers[106][107] and to distinguish highly invasive cancer cell lines from less invasive lines using only cell shape information.[108][109]

 ANNs have been used to accelerate reliability analysis of infrastructures subject to natural disasters[110][111] and to predict foundation settlements.[112] ANNs have also been used for building black-box models in geoscience: hydrology,[113][114] ocean modelling and coastal engineering,[115][116] and geomorphology.[117] ANNs have been employed in cybersecurity, with the objective to discriminate between legitimate activities and malicious ones. For example, machine learning has been used for classifying Android malware,[118] for identifying domains belonging to threat actors and for detecting URLs posing a security risk.[119] Research is underway on ANN systems designed for penetration testing, for detecting botnets,[120] credit cards frauds[121] and network intrusions.

 ANNs have been proposed as a tool to solve partial differential equations in physics[122][123][124] and simulate the properties of many-body open quantum systems.[125][126][127][128] In brain research ANNs have studied short-term behavior of individual neurons,[129] the dynamics of neural circuitry arise from interactions between individual neurons and how behavior can arise from abstract neural modules that represent complete subsystems. Studies considered long-and short-term plasticity of neural systems and their relation to learning and memory from the individual neuron to the system level.

 Theoretical properties [ edit ]

 Computational power [ edit ]

 The multilayer perceptron is a universal function approximator, as proven by the universal approximation theorem. However, the proof is not constructive regarding the number of neurons required, the network topology, the weights and the learning parameters.

 A specific recurrent architecture with rational-valued weights (as opposed to full precision real number-valued weights) has the power of a universal Turing machine,[130] using a finite number of neurons and standard linear connections. Further, the use of irrational values for weights results in a machine with super-Turing power.[131]

 Capacity [ edit ]

 A model's "capacity" property corresponds to its ability to model any given function. It is related to the amount of information that can be stored in the network and to the notion of complexity. Two notions of capacity are known by the community. The information capacity and the VC Dimension. The information capacity of a perceptron is intensively discussed in Sir David MacKay's book[132] which summarizes work by Thomas Cover.[133] The capacity of a network of standard neurons (not convolutional) can be derived by four rules[134] that derive from understanding a neuron as an electrical element. The information capacity captures the functions modelable by the network given any data as input. The second notion, is the VC dimension. VC Dimension uses the principles of measure theory and finds the maximum capacity under the best possible circumstances. This is, given input data in a specific form. As noted in,[132] the VC Dimension for arbitrary inputs is half the information capacity of a Perceptron. The VC Dimension for arbitrary points is sometimes referred to as Memory Capacity.[135]

 Convergence [ edit ]

 Models may not consistently converge on a single solution, firstly because local minima may exist, depending on the cost function and the model. Secondly, the optimization method used might not guarantee to converge when it begins far from any local minimum. Thirdly, for sufficiently large data or parameters, some methods become impractical.

 Another issue worthy to mention is that training may cross some Saddle point which may lead the convergence to the wrong direction.

 The convergence behavior of certain types of ANN architectures are more understood than others. When the width of network approaches to infinity, the ANN is well described by its first order Taylor expansion throughout training, and so inherits the convergence behavior of affine models.[136][137] Another example is when parameters are small, it is observed that ANNs often fits target functions from low to high frequencies. This behavior is referred to as the spectral bias, or frequency principle, of neural networks.[138][139][140][141] This phenomenon is the opposite to the behavior of some well studied iterative numerical schemes such as Jacobi method. Deeper neural networks have been observed to be more biased towards low frequency functions.[142]

 Generalization and statistics [ edit ]

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 Applications whose goal is to create a system that generalizes well to unseen examples, face the possibility of over-training. This arises in convoluted or over-specified systems when the network capacity significantly exceeds the needed free parameters. Two approaches address over-training. The first is to use cross-validation and similar techniques to check for the presence of over-training and to select hyperparameters to minimize the generalization error.

 The second is to use some form of regularization. This concept emerges in a probabilistic (Bayesian) framework, where regularization can be performed by selecting a larger prior probability over simpler models; but also in statistical learning theory, where the goal is to minimize over two quantities: the 'empirical risk' and the 'structural risk', which roughly corresponds to the error over the training set and the predicted error in unseen data due to overfitting.

 Confidence analysis of a neural network

 Supervised neural networks that use a mean squared error (MSE) cost function can use formal statistical methods to determine the confidence of the trained model. The MSE on a validation set can be used as an estimate for variance. This value can then be used to calculate the confidence interval of network output, assuming a normal distribution. A confidence analysis made this way is statistically valid as long as the output probability distribution stays the same and the network is not modified.

 By assigning a softmax activation function, a generalization of the logistic function, on the output layer of the neural network (or a softmax component in a component-based network) for categorical target variables, the outputs can be interpreted as posterior probabilities. This is useful in classification as it gives a certainty measure on classifications.

 The softmax activation function is:


 Criticism [ edit ]

 Training [ edit ]

 A common criticism of neural networks, particularly in robotics, is that they require too much training for real-world operation.[ citation needed ] Potential solutions include randomly shuffling training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections following an example, grouping examples in so-called mini-batches and/or introducing a recursive least squares algorithm for CMAC.[81]

 Theory [ edit ]

 A central claim[ citation needed ] of ANNs is that they embody new and powerful general principles for processing information. These principles are ill-defined. It is often claimed[ by whom? ] that they are emergent from the network itself. This allows simple statistical association (the basic function of artificial neural networks) to be described as learning or recognition. In 1997, Alexander Dewdney commented that, as a result, artificial neural networks have a "something-for-nothing quality, one that imparts a peculiar aura of laziness and a distinct lack of curiosity about just how good these computing systems are. No human hand (or mind) intervenes; solutions are found as if by magic; and no one, it seems, has learned anything".[143] One response to Dewdney is that neural networks handle many complex and diverse tasks, ranging from autonomously flying aircraft[144] to detecting credit card fraud to mastering the game of Go.

 Technology writer Roger Bridgman commented:

 Neural networks, for instance, are in the dock not only because they have been hyped to high heaven, (what hasn't?) but also because you could create a successful net without understanding how it worked: the bunch of numbers that captures its behaviour would in all probability be "an opaque, unreadable table...valueless as a scientific resource".

 In spite of his emphatic declaration that science is not technology, Dewdney seems here to pillory neural nets as bad science when most of those devising them are just trying to be good engineers. An unreadable table that a useful machine could read would still be well worth having.[145]

 Biological brains use both shallow and deep circuits as reported by brain anatomy,[146] displaying a wide variety of invariance. Weng[147] argued that the brain self-wires largely according to signal statistics and therefore, a serial cascade cannot catch all major statistical dependencies.

 Hardware [ edit ]

 Large and effective neural networks require considerable computing resources.[148] While the brain has hardware tailored to the task of processing signals through a graph of neurons, simulating even a simplified neuron on von Neumann architecture may consume vast amounts of memory and storage. Furthermore, the designer often needs to transmit signals through many of these connections and their associated neurons – which require enormous CPU power and time.

 Schmidhuber noted that the resurgence of neural networks in the twenty-first century is largely attributable to advances in hardware: from 1991 to 2015, computing power, especially as delivered by GPGPUs (on GPUs), has increased around a million-fold, making the standard backpropagation algorithm feasible for training networks that are several layers deeper than before.[12] The use of accelerators such as FPGAs and GPUs can reduce training times from months to days.[148]

 Neuromorphic engineering or a physical neural network addresses the hardware difficulty directly, by constructing non-von-Neumann chips to directly implement neural networks in circuitry. Another type of chip optimized for neural network processing is called a Tensor Processing Unit, or TPU.[149]

 Practical counterexamples [ edit ]

 Analyzing what has been learned by an ANN is much easier than analyzing what has been learned by a biological neural network. Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering general principles that allow a learning machine to be successful. For example, local vs. non-local learning and shallow vs. deep architecture.[150]

 Hybrid approaches [ edit ]

 Advocates of hybrid models (combining neural networks and symbolic approaches) say that such a mixture can better capture the mechanisms of the human mind.[151]

 Gallery [ edit ]

 * A single-layer feedforward artificial neural network. Arrows originating from are omitted for clarity. There are p inputs to this network and q outputs. In this system, the value of the qth output, would be calculated as .

 * A two-layer feedforward artificial neural network

 * An artificial neural network

 * An ANN dependency graph

 * A single-layer feedforward artificial neural network with 4 inputs, 6 hidden and 2 outputs. Given position state and direction outputs wheel based control values.

 * A two-layer feedforward artificial neural network with 8 inputs, 2x8 hidden and 2 outputs. Given position state, direction and other environment values outputs thruster based control values.

 * Parallel pipeline structure of CMAC neural network. This learning algorithm can converge in one step.

 See also [ edit ]

 * ADALINE
 * Artificial philosophy
 * Autoencoder
 * Bio-inspired computing
 * Blue Brain Project
 * Catastrophic interference
 * Cognitive architecture
 * Connectionist expert system
 * Connectomics
 * Large width limits of neural networks
 * List of machine learning concepts
 * Neural gas
 * Neural network software
 * Optical neural network
 * Parallel distributed processing
 * Recurrent neural networks
 * Spiking neural network
 * Tensor product network

 Notes [ edit ]

 1. ^ Steering for the 1995 " No Hands Across America " required "only a few human assists".

 References [ edit ]

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An artificial neural network is an interconnected group of nodes, inspired by a simplification of neurons in a brain. Here, each circular node represents an artificial neuron and an arrow represents a connection from the output of one artificial neuron to the input of another.  
 Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, [1]  are computing systems inspired by the biological neural networks that constitute animal brains. [2] 
 An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons. An artificial neuron receives signals then processes them and can signal neurons connected to it. The "signal" at a connection is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs. The connections are called edges. Neurons and edges typically have a  weight  that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Neurons may have a threshold such that a signal is sent only if the aggregate signal crosses that threshold.
 
Typically, neurons are aggregated into layers. Different layers may perform different transformations on their inputs. Signals travel from the first layer (the input layer), to the last layer (the output layer), possibly after traversing the layers multiple times.
Training[edit]
 Neural networks learn (or are trained) by processing examples, each of which contains a known "input" and "result," forming probability-weighted associations between the two, which are stored within the data structure of the net itself. The training of a neural network from a given example is usually conducted by determining the difference between the processed output of the network (often a prediction) and a target output. This difference is the error. The network then adjusts its weighted associations according to a learning rule and using this error value. Successive adjustments will cause the neural network to produce output that is increasingly similar to the target output. After a sufficient number of these adjustments, the training can be terminated based on certain criteria. This is known as supervised learning.
 Such systems "learn" to perform tasks by considering examples, generally without being programmed with task-specific rules. For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as "cat" or "no cat" and using the results to identify cats in other images. They do this without any prior knowledge of cats, for example, that they have fur, tails, whiskers, and cat-like faces. Instead, they automatically generate identifying characteristics from the examples that they process.
History[edit]
 Warren McCulloch and Walter Pitts  [3]  (1943) opened the subject by creating a computational model for neural networks. [4]  In the late 1940s, D. O. Hebb  [5]  created a learning hypothesis based on the mechanism of neural plasticity that became known as Hebbian learning. Farley and Wesley A. Clark  [6]  (1954) first used computational machines, then called "calculators", to simulate a Hebbian network. In 1958, psychologist Frank Rosenblatt invented the perceptron, the first artificial neural network, [7]   [8]   [9]   [10]  funded by the United States Office of Naval Research. [11]  The first functional networks with many layers were published by Ivakhnenko and Lapa in 1965, as the Group Method of Data Handling. [12]   [13]   [14]  The basics of continuous backpropagation [12]   [15]   [16]   [17]  were derived in the context of control theory by Kelley  [18]  in 1960 and by Bryson in 1961, [19]  using principles of dynamic programming. Thereafter research stagnated following Minsky and Papert (1969), [20]  who discovered that basic perceptrons were incapable of processing the exclusive-or circuit and that computers lacked sufficient power to process useful neural networks.
 In 1970, Seppo Linnainmaa published the general method for automatic differentiation (AD) of discrete connected networks of nested differentiable functions. [21]   [22]  In 1973, Dreyfus used backpropagation to adapt parameters of controllers in proportion to error gradients. [23]  Werbos's (1975) backpropagation algorithm enabled practical training of multi-layer networks. In 1982, he applied Linnainmaa's AD method to neural networks in the way that became widely used. [15]   [24] 
 The development of metal–oxide–semiconductor (MOS) very-large-scale integration (VLSI), in the form of complementary MOS (CMOS) technology, enabled increasing MOS transistor counts in digital electronics. This provided more processing power for the development of practical artificial neural networks in the 1980s. [25] 
 In 1986 Rumelhart, Hinton and Williams showed that backpropagation learned interesting internal representations of words as feature vectors when trained to predict the next word in a sequence. [26] 
 From 1988 onward, [27]   [28]  the use of neural networks transformed the field of protein structure prediction, in particular when the first cascading networks were trained on profiles (matrices) produced by multiple sequence alignments. [29] 
 In 1992, max-pooling was introduced to help with least-shift invariance and tolerance to deformation to aid 3D object recognition. [30]   [31]   [32]  Schmidhuber adopted a multi-level hierarchy of networks (1992) pre-trained one level at a time by unsupervised learning and fine-tuned by backpropagation. [33] 
 Neural networks' early successes included predicting the stock market and in 1995 a (mostly) self-driving car. [a]   [34] 
  Geoffrey Hinton et al. (2006) proposed learning a high-level representation using successive layers of binary or real-valued latent variables with a restricted Boltzmann machine  [35]  to model each layer. In 2012, Ng and Dean created a network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images. [36]  Unsupervised pre-training and increased computing power from GPUs and distributed computing allowed the use of larger networks, particularly in image and visual recognition problems, which became known as "deep learning". [37] 
 Ciresan and colleagues (2010) [38]  showed that despite the vanishing gradient problem, GPUs make backpropagation feasible for many-layered feedforward neural networks. [39]  Between 2009 and 2012, ANNs began winning prizes in image recognition contests, approaching human level performance on various tasks, initially in pattern recognition and handwriting recognition. [40]   [41]  For example, the bi-directional and multi-dimensional long short-term memory (LSTM) [42]   [43]  of Graves et al. won three competitions in connected handwriting recognition in 2009 without any prior knowledge about the three languages to be learned. [42]   [43] 
 Ciresan and colleagues built the first pattern recognizers to achieve human-competitive/superhuman performance [44]  on benchmarks such as traffic sign recognition (IJCNN 2012).
Models[edit]
      Neuron and myelinated axon, with signal flow from inputs at dendrites to outputs at axon terminals  
ANNs began as an attempt to exploit the architecture of the human brain to perform tasks that conventional algorithms had little success with. They soon reoriented towards improving empirical results, mostly abandoning attempts to remain true to their biological precursors. Neurons are connected to each other in various patterns, to allow the output of some neurons to become the input of others. The network forms a directed, weighted graph. [45] 
 An artificial neural network consists of a collection of simulated neurons. Each neuron is a node which is connected to other nodes via links that correspond to biological axon-synapse-dendrite connections. Each link has a weight, which determines the strength of one node's influence on another. [46] 
Artificial neurons[edit]
ANNs are composed of artificial neurons which are conceptually derived from biological neurons. Each artificial neuron has inputs and produces a single output which can be sent to multiple other neurons. [47]  The inputs can be the feature values of a sample of external data, such as images or documents, or they can be the outputs of other neurons. The outputs of the final output neurons of the neural net accomplish the task, such as recognizing an object in an image.
 To find the output of the neuron we take the weighted sum of all the inputs, weighted by the weights of the connections from the inputs to the neuron. We add a bias term to this sum. [48]  This weighted sum is sometimes called the activation. This weighted sum is then passed through a (usually nonlinear) activation function to produce the output. The initial inputs are external data, such as images and documents. The ultimate outputs accomplish the task, such as recognizing an object in an image. [49] 
Organization[edit]
The neurons are typically organized into multiple layers, especially in deep learning. Neurons of one layer connect only to neurons of the immediately preceding and immediately following layers. The layer that receives external data is the input layer. The layer that produces the ultimate result is the output layer. In between them are zero or more hidden layers. Single layer and unlayered networks are also used. Between two layers, multiple connection patterns are possible. They can be 'fully connected', with every neuron in one layer connecting to every neuron in the next layer. They can be pooling, where a group of neurons in one layer connect to a single neuron in the next layer, thereby reducing the number of neurons in that layer. [50]  Neurons with only such connections form a directed acyclic graph and are known as  feedforward networks . [51]  Alternatively, networks that allow connections between neurons in the same or previous layers are known as  recurrent networks  . [52]  
Hyperparameter[edit]
A hyperparameter is a constant parameter whose value is set before the learning process begins. The values of parameters are derived via learning. Examples of hyperparameters include learning rate, the number of hidden layers and batch size. [53]  The values of some hyperparameters can be dependent on those of other hyperparameters. For example, the size of some layers can depend on the overall number of layers.
Learning[edit]
Learning is the adaptation of the network to better handle a task by considering sample observations. Learning involves adjusting the weights (and optional thresholds) of the network to improve the accuracy of the result. This is done by minimizing the observed errors. Learning is complete when examining additional observations does not usefully reduce the error rate. Even after learning, the error rate typically does not reach 0. If after learning, the error rate is too high, the network typically must be redesigned. Practically this is done by defining a cost function that is evaluated periodically during learning. As long as its output continues to decline, learning continues. The cost is frequently defined as a statistic whose value can only be approximated. The outputs are actually numbers, so when the error is low, the difference between the output (almost certainly a cat) and the correct answer (cat) is small. Learning attempts to reduce the total of the differences across the observations. Most learning models can be viewed as a straightforward application of optimization theory and statistical estimation. [45]   [54] 
Learning rate[edit]
The learning rate defines the size of the corrective steps that the model takes to adjust for errors in each observation. [55]  A high learning rate shortens the training time, but with lower ultimate accuracy, while a lower learning rate takes longer, but with the potential for greater accuracy. Optimizations such as Quickprop are primarily aimed at speeding up error minimization, while other improvements mainly try to increase reliability. In order to avoid oscillation inside the network such as alternating connection weights, and to improve the rate of convergence, refinements use an adaptive learning rate that increases or decreases as appropriate. [56]  The concept of momentum allows the balance between the gradient and the previous change to be weighted such that the weight adjustment depends to some degree on the previous change. A momentum close to 0 emphasizes the gradient, while a value close to 1 emphasizes the last change.
Cost function[edit]
While it is possible to define a cost function ad hoc, frequently the choice is determined by the function's desirable properties (such as convexity) or because it arises from the model (e.g. in a probabilistic model the model's posterior probability can be used as an inverse cost).
Backpropagation[edit]
Backpropagation is a method used to adjust the connection weights to compensate for each error found during learning. The error amount is effectively divided among the connections. Technically, backprop calculates the gradient (the derivative) of the cost function associated with a given state with respect to the weights. The weight updates can be done via stochastic gradient descent or other methods, such as Extreme Learning Machines, [57]  "No-prop" networks, [58]  training without backtracking, [59]  "weightless" networks, [60]   [61]  and non-connectionist neural networks.[ citation needed ]
Learning paradigms[edit]
Machine learning is commonly separated into three main learning paradigms, supervised learning, unsupervised learning and reinforcement learning. [62]  Each corresponds to a particular learning task.
Supervised learning[edit]
 Supervised learning uses a set of paired inputs and desired outputs. The learning task is to produce the desired output for each input. In this case, the cost function is related to eliminating incorrect deductions. [63]  A commonly used cost is the mean-squared error, which tries to minimize the average squared error between the network's output and the desired output. Tasks suited for supervised learning are pattern recognition (also known as classification) and regression (also known as function approximation). Supervised learning is also applicable to sequential data (e.g., for hand writing, speech and gesture recognition). This can be thought of as learning with a "teacher", in the form of a function that provides continuous feedback on the quality of solutions obtained thus far.
Unsupervised learning[edit]
In unsupervised learning, input data is given along with the cost function, some function of the data and the network's output. The cost function is dependent on the task (the model domain) and any  a priori  assumptions (the implicit properties of the model, its parameters and the observed variables). As a trivial example, consider the model where is a constant and the cost . Minimizing this cost produces a value of that is equal to the mean of the data. The cost function can be much more complicated. Its form depends on the application: for example, in compression it could be related to the mutual information between and , whereas in statistical modeling, it could be related to the posterior probability of the model given the data (note that in both of those examples, those quantities would be maximized rather than minimized). Tasks that fall within the paradigm of unsupervised learning are in general estimation problems; the applications include clustering, the estimation of statistical distributions, compression and filtering.
Reinforcement learning[edit]
In applications such as playing video games, an actor takes a string of actions, receiving a generally unpredictable response from the environment after each one. The goal is to win the game, i.e., generate the most positive (lowest cost) responses. In reinforcement learning, the aim is to weight the network (devise a policy) to perform actions that minimize long-term (expected cumulative) cost. At each point in time the agent performs an action and the environment generates an observation and an instantaneous cost, according to some (usually unknown) rules. The rules and the long-term cost usually only can be estimated. At any juncture, the agent decides whether to explore new actions to uncover their costs or to exploit prior learning to proceed more quickly.
 Formally the environment is modeled as a Markov decision process (MDP) with states and actions . Because the state transitions are not known, probability distributions are used instead: the instantaneous cost distribution , the observation distribution and the transition distribution , while a policy is defined as the conditional distribution over actions given the observations. Taken together, the two define a Markov chain (MC). The aim is to discover the lowest-cost MC.
 ANNs serve as the learning component in such applications. [64]   [65]  Dynamic programming coupled with ANNs (giving neurodynamic programming) [66]  has been applied to problems such as those involved in vehicle routing, [67]  video games, natural resource management  [68]   [69]  and medicine  [70]  because of ANNs ability to mitigate losses of accuracy even when reducing the discretization grid density for numerically approximating the solution of control problems. Tasks that fall within the paradigm of reinforcement learning are control problems, games and other sequential decision making tasks.
Self-learning[edit]
Self-learning in neural networks was introduced in 1982 along with a neural network capable of self-learning named Crossbar Adaptive Array (CAA). [71]  It is a system with only one input, situation s, and only one output, action (or behavior) a. It has neither external advice input nor external reinforcement input from the environment. The CAA computes, in a crossbar fashion, both decisions about actions and emotions (feelings) about encountered situations. The system is driven by the interaction between cognition and emotion. [72]  Given the memory matrix, W =||w(a,s)||, the crossbar self-learning algorithm in each iteration performs the following computation:
 In situation s perform action a;
 Receive consequence situation s';
 Compute emotion of being in consequence situation v(s');
 Update crossbar memory w'(a,s) = w(a,s) + v(s').
The backpropagated value (secondary reinforcement) is the emotion toward the consequence situation. The CAA exists in two environments, one is behavioral environment where it behaves, and the other is genetic environment, where from it initially and only once receives initial emotions about to be encountered situations in the behavioral environment. Having received the genome vector (species vector) from the genetic environment, the CAA will learn a goal-seeking behavior, in the behavioral environment that contains both desirable and undesirable situations. [73] 
Neuroevolution[edit]
 Neuroevolution can create neural network topologies and weights using evolutionary computation. It is competitive with sophisticated gradient descent approaches[ citation needed ]. One advantage of neuroevolution is that it may be less prone to get caught in "dead ends". [74] 
Stochastic neural network[edit]
 Stochastic neural networks originating from Sherrington–Kirkpatrick models are a type of artificial neural network built by introducing random variations into the network, either by giving the network's artificial neurons stochastic transfer functions, or by giving them stochastic weights. This makes them useful tools for optimization problems, since the random fluctuations help the network escape from local minima. [75]  Stochastic neural networks trained using a Bayesian approach are known as Bayesian neural networks. [76] 
Other[edit]
In a Bayesian framework, a distribution over the set of allowed models is chosen to minimize the cost. Evolutionary methods, [77]  gene expression programming, [78]  simulated annealing, [79]  expectation-maximization, non-parametric methods and particle swarm optimization  [80]  are other learning algorithms. Convergent recursion is a learning algorithm for cerebellar model articulation controller (CMAC) neural networks. [81]   [82] 
Modes[edit]
Two modes of learning are available: stochastic and batch. In stochastic learning, each input creates a weight adjustment. In batch learning weights are adjusted based on a batch of inputs, accumulating errors over the batch. Stochastic learning introduces "noise" into the process, using the local gradient calculated from one data point; this reduces the chance of the network getting stuck in local minima. However, batch learning typically yields a faster, more stable descent to a local minimum, since each update is performed in the direction of the batch's average error. A common compromise is to use "mini-batches", small batches with samples in each batch selected stochastically from the entire data set.
Types[edit]
ANNs have evolved into a broad family of techniques that have advanced the state of the art across multiple domains. The simplest types have one or more static components, including number of units, number of layers, unit weights and topology. Dynamic types allow one or more of these to evolve via learning. The latter are much more complicated, but can shorten learning periods and produce better results. Some types allow/require learning to be "supervised" by the operator, while others operate independently. Some types operate purely in hardware, while others are purely software and run on general purpose computers.
 Some of the main breakthroughs include: convolutional neural networks that have proven particularly successful in processing visual and other two-dimensional data; [83]   [84]  long short-term memory avoid the vanishing gradient problem  [85]  and can handle signals that have a mix of low and high frequency components aiding large-vocabulary speech recognition, [86]   [87]  text-to-speech synthesis, [88]   [15]   [89]  and photo-real talking heads; [90]  competitive networks such as generative adversarial networks in which multiple networks (of varying structure) compete with each other, on tasks such as winning a game [91]  or on deceiving the opponent about the authenticity of an input. [92] 
Network design[edit]
Neural architecture search (NAS) uses machine learning to automate ANN design. Various approaches to NAS have designed networks that compare well with hand-designed systems. The basic search algorithm is to propose a candidate model, evaluate it against a dataset and use the results as feedback to teach the NAS network. [93]  Available systems include AutoML and AutoKeras. [94] 
 Design issues include deciding the number, type and connectedness of network layers, as well as the size of each and the connection type (full, pooling, ...).
  Hyperparameters must also be defined as part of the design (they are not learned), governing matters such as how many neurons are in each layer, learning rate, step, stride, depth, receptive field and padding (for CNNs), etc. [95] 
Use[edit]
Using Artificial neural networks requires an understanding of their characteristics.
 Choice of model: This depends on the data representation and the application. Overly complex models are slow learning.
Learning algorithm: Numerous trade-offs exist between learning algorithms. Almost any algorithm will work well with the correct hyperparameters for training on a particular data set. However, selecting and tuning an algorithm for training on unseen data requires significant experimentation.
Robustness: If the model, cost function and learning algorithm are selected appropriately, the resulting ANN can become robust. 
ANN capabilities fall within the following broad categories:[ citation needed ]
  Function approximation, or regression analysis, including time series prediction, fitness approximation and modeling.
 Classification, including pattern and sequence recognition, novelty detection and sequential decision making. [96]  
 Data processing, including filtering, clustering, blind source separation and compression.
 Robotics, including directing manipulators and prostheses. 
Applications[edit]
Because of their ability to reproduce and model nonlinear processes, artificial neural networks have found applications in many disciplines. Application areas include system identification and control (vehicle control, trajectory prediction, [97]  process control, natural resource management), quantum chemistry, [98]  general game playing, [99]  pattern recognition (radar systems, face identification, signal classification, [100]  3D reconstruction, [101]  object recognition and more), sensor data analysis, [102]  sequence recognition (gesture, speech, handwritten and printed text recognition [103] ), medical diagnosis, finance [104]  (e.g. automated trading systems), data mining, visualization, machine translation, social network filtering [105]  and e-mail spam filtering. ANNs have been used to diagnose several types of cancers [106]   [107]  and to distinguish highly invasive cancer cell lines from less invasive lines using only cell shape information. [108]   [109] 
 ANNs have been used to accelerate reliability analysis of infrastructures subject to natural disasters [110]   [111]  and to predict foundation settlements. [112]  ANNs have also been used for building black-box models in geoscience: hydrology, [113]   [114]  ocean modelling and coastal engineering, [115]   [116]  and geomorphology. [117]  ANNs have been employed in cybersecurity, with the objective to discriminate between legitimate activities and malicious ones. For example, machine learning has been used for classifying Android malware, [118]  for identifying domains belonging to threat actors and for detecting URLs posing a security risk. [119]  Research is underway on ANN systems designed for penetration testing, for detecting botnets, [120]  credit cards frauds [121]  and network intrusions.
 ANNs have been proposed as a tool to solve partial differential equations in physics [122]   [123]   [124]  and simulate the properties of many-body open quantum systems. [125]   [126]   [127]   [128]  In brain research ANNs have studied short-term behavior of individual neurons, [129]  the dynamics of neural circuitry arise from interactions between individual neurons and how behavior can arise from abstract neural modules that represent complete subsystems. Studies considered long-and short-term plasticity of neural systems and their relation to learning and memory from the individual neuron to the system level.
Theoretical properties[edit]
Computational power[edit]
The multilayer perceptron is a universal function approximator, as proven by the universal approximation theorem. However, the proof is not constructive regarding the number of neurons required, the network topology, the weights and the learning parameters.
 A specific recurrent architecture with rational-valued weights (as opposed to full precision real number-valued weights) has the power of a universal Turing machine, [130]  using a finite number of neurons and standard linear connections. Further, the use of irrational values for weights results in a machine with super-Turing power. [131] 
Capacity[edit]
A model's "capacity" property corresponds to its ability to model any given function. It is related to the amount of information that can be stored in the network and to the notion of complexity.
Two notions of capacity are known by the community. The information capacity and the VC Dimension. The information capacity of a perceptron is intensively discussed in Sir David MacKay's book [132]  which summarizes work by Thomas Cover. [133]  The capacity of a network of standard neurons (not convolutional) can be derived by four rules [134]  that derive from understanding a neuron as an electrical element. The information capacity captures the functions modelable by the network given any data as input. The second notion, is the VC dimension. VC Dimension uses the principles of measure theory and finds the maximum capacity under the best possible circumstances. This is, given input data in a specific form. As noted in, [132]  the VC Dimension for arbitrary inputs is half the information capacity of a Perceptron. The VC Dimension for arbitrary points is sometimes referred to as Memory Capacity. [135] 
Convergence[edit]
Models may not consistently converge on a single solution, firstly because local minima may exist, depending on the cost function and the model. Secondly, the optimization method used might not guarantee to converge when it begins far from any local minimum. Thirdly, for sufficiently large data or parameters, some methods become impractical.
 Another issue worthy to mention is that training may cross some Saddle point which may lead the convergence to the wrong direction.
 The convergence behavior of certain types of ANN architectures are more understood than others. When the width of network approaches to infinity, the ANN is well described by its first order Taylor expansion throughout training, and so inherits the convergence behavior of affine models. [136]   [137]  Another example is when parameters are small, it is observed that ANNs often fits target functions from low to high frequencies. This behavior is referred to as the spectral bias, or frequency principle, of neural networks. [138]   [139]   [140]   [141]  This phenomenon is the opposite to the behavior of some well studied iterative numerical schemes such as Jacobi method. Deeper neural networks have been observed to be more biased towards low frequency functions. [142] 
Generalization and statistics[edit]
Applications whose goal is to create a system that generalizes well to unseen examples, face the possibility of over-training. This arises in convoluted or over-specified systems when the network capacity significantly exceeds the needed free parameters. Two approaches address over-training. The first is to use cross-validation and similar techniques to check for the presence of over-training and to select hyperparameters to minimize the generalization error.
 The second is to use some form of  regularization . This concept emerges in a probabilistic (Bayesian) framework, where regularization can be performed by selecting a larger prior probability over simpler models; but also in statistical learning theory, where the goal is to minimize over two quantities: the 'empirical risk' and the 'structural risk', which roughly corresponds to the error over the training set and the predicted error in unseen data due to overfitting.
      Confidence analysis of a neural network  
Supervised neural networks that use a mean squared error (MSE) cost function can use formal statistical methods to determine the confidence of the trained model. The MSE on a validation set can be used as an estimate for variance. This value can then be used to calculate the confidence interval of network output, assuming a normal distribution. A confidence analysis made this way is statistically valid as long as the output probability distribution stays the same and the network is not modified.
 By assigning a softmax activation function, a generalization of the logistic function, on the output layer of the neural network (or a softmax component in a component-based network) for categorical target variables, the outputs can be interpreted as posterior probabilities. This is useful in classification as it gives a certainty measure on classifications.
 The softmax activation function is:
   
Criticism[edit]
Training[edit]
A common criticism of neural networks, particularly in robotics, is that they require too much training for real-world operation.[ citation needed ] Potential solutions include randomly shuffling training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections following an example, grouping examples in so-called mini-batches and/or introducing a recursive least squares algorithm for CMAC. [81] 
Theory[edit]
A central claim[ citation needed ] of ANNs is that they embody new and powerful general principles for processing information. These principles are ill-defined. It is often claimed[ by whom? ] that they are emergent from the network itself. This allows simple statistical association (the basic function of artificial neural networks) to be described as learning or recognition. In 1997, Alexander Dewdney commented that, as a result, artificial neural networks have a "something-for-nothing quality, one that imparts a peculiar aura of laziness and a distinct lack of curiosity about just how good these computing systems are. No human hand (or mind) intervenes; solutions are found as if by magic; and no one, it seems, has learned anything". [143]  One response to Dewdney is that neural networks handle many complex and diverse tasks, ranging from autonomously flying aircraft [144]  to detecting credit card fraud to mastering the game of Go.
 Technology writer Roger Bridgman commented:
 Neural networks, for instance, are in the dock not only because they have been hyped to high heaven, (what hasn't?) but also because you could create a successful net without understanding how it worked: the bunch of numbers that captures its behaviour would in all probability be "an opaque, unreadable table...valueless as a scientific resource".
 In spite of his emphatic declaration that science is not technology, Dewdney seems here to pillory neural nets as bad science when most of those devising them are just trying to be good engineers. An unreadable table that a useful machine could read would still be well worth having. [145] 
Biological brains use both shallow and deep circuits as reported by brain anatomy, [146]  displaying a wide variety of invariance. Weng [147]  argued that the brain self-wires largely according to signal statistics and therefore, a serial cascade cannot catch all major statistical dependencies.
Hardware[edit]
Large and effective neural networks require considerable computing resources. [148]  While the brain has hardware tailored to the task of processing signals through a graph of neurons, simulating even a simplified neuron on von Neumann architecture may consume vast amounts of memory and storage. Furthermore, the designer often needs to transmit signals through many of these connections and their associated neurons – which require enormous CPU power and time.
  Schmidhuber noted that the resurgence of neural networks in the twenty-first century is largely attributable to advances in hardware: from 1991 to 2015, computing power, especially as delivered by GPGPUs (on GPUs), has increased around a million-fold, making the standard backpropagation algorithm feasible for training networks that are several layers deeper than before. [12]  The use of accelerators such as FPGAs and GPUs can reduce training times from months to days. [148] 
  Neuromorphic engineering or a physical neural network addresses the hardware difficulty directly, by constructing non-von-Neumann chips to directly implement neural networks in circuitry. Another type of chip optimized for neural network processing is called a Tensor Processing Unit, or TPU. [149] 
Practical counterexamples[edit]
Analyzing what has been learned by an ANN is much easier than analyzing what has been learned by a biological neural network. Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering general principles that allow a learning machine to be successful. For example, local vs. non-local learning and shallow vs. deep architecture. [150] 
Hybrid approaches[edit]
Advocates of hybrid models (combining neural networks and symbolic approaches) say that such a mixture can better capture the mechanisms of the human mind. [151] 
Gallery[edit]
	 
	     
	A single-layer feedforward artificial neural network. Arrows originating from are omitted for clarity. There are p inputs to this network and q outputs. In this system, the value of the qth output, would be calculated as .
	 
	 
	     
	A two-layer feedforward artificial neural network
	 
	 
	     
	An artificial neural network
	 
	 
	     
	An ANN dependency graph
	 
	 
	     
	A single-layer feedforward artificial neural network with 4 inputs, 6 hidden and 2 outputs. Given position state and direction outputs wheel based control values.
	 
	 
	     
	A two-layer feedforward artificial neural network with 8 inputs, 2x8 hidden and 2 outputs. Given position state, direction and other environment values outputs thruster based control values.
	 
	 
	     
	Parallel pipeline structure of CMAC neural network. This learning algorithm can converge in one step.
	 
See also[edit]
  ADALINE 
Artificial philosophy
 Autoencoder 
 Bio-inspired computing 
 Blue Brain Project 
 Catastrophic interference 
 Cognitive architecture 
 Connectionist expert system 
 Connectomics 
 Large width limits of neural networks 
 List of machine learning concepts 
 Neural gas 
 Neural network software 
 Optical neural network 
 Parallel distributed processing 
 Recurrent neural networks 
 Spiking neural network 
 Tensor product network  
Notes[edit]
 
  ^  Steering for the 1995 "No Hands Across America" required "only a few human assists".
 
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Artificial neural network - Wikipedia
https://en.wikipedia.org/wiki/Artificial_neural_network
https://en.wikipedia.org/wiki/Machine_learning
Machine learning - Wikipedia
2003-05-25
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<div><div>
<p><b>Machine learning</b> (<b>ML</b>) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks.<sup><a href="#cite_note-1">[1]</a></sup> It is seen as a part of <a href="/wiki/Artificial_intelligence">artificial intelligence</a>. 
</p><p>Machine learning algorithms build a model based on sample data, known as <a href="/wiki/Training_data">training data</a>, in order to make predictions or decisions without being explicitly programmed to do so.<sup><a href="#cite_note-2">[2]</a></sup> Machine learning algorithms are used in a wide variety of applications, such as in medicine, <a href="/wiki/Email_filtering">email filtering</a>, <a href="/wiki/Speech_recognition">speech recognition</a>, <a href="/wiki/Agriculture">agriculture</a>, and <a href="/wiki/Computer_vision">computer vision</a>, where it is difficult or unfeasible to develop conventional algorithms to perform the needed tasks.<sup><a href="#cite_note-tvt-3">[3]</a></sup><sup><a href="#cite_note-4">[4]</a></sup>
</p><p>A subset of machine learning is closely related to <a href="/wiki/Computational_statistics">computational statistics</a>, which focuses on making predictions using computers, but not all machine learning is statistical learning. The study of <a href="/wiki/Mathematical_optimization">mathematical optimization</a> delivers methods, theory and application domains to the field of machine learning. <a href="/wiki/Data_mining">Data mining</a> is a related field of study, focusing on <a href="/wiki/Exploratory_data_analysis">exploratory data analysis</a> through <a href="/wiki/Unsupervised_learning">unsupervised learning</a>.<sup><a href="#cite_note-6">[6]</a></sup><sup><a href="#cite_note-7">[7]</a></sup> 
</p><p>Some implementations of machine learning use data and <a href="/wiki/Neural_networks">neural networks</a> in a way that mimics the working of a <a href="/wiki/Brain">biological brain</a>.<sup><a href="#cite_note-8">[8]</a></sup><sup><a href="#cite_note-9">[9]</a></sup> 
</p><p>In its application across business problems, machine learning is also referred to as <a href="/wiki/Predictive_analytics">predictive analytics</a>.
</p>
<h2>Overview[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=1">edit</a>]</h2>
<p>Learning algorithms work on the basis that strategies, algorithms, and inferences that worked well in the past are likely to continue working well in the future. These inferences can be obvious, such as "since the sun rose every morning for the last 10,000 days, it will probably rise tomorrow morning as well". They can be nuanced, such as "X% of <a href="/wiki/Family_(biology)">families</a> have geographically separate species with color variants, so there is a Y% chance that undiscovered <a href="/wiki/Black_swan_theory">black swans</a> exist".<sup><a href="#cite_note-FOOTNOTEDomingos2015Chapter_6,_Chapter_7-10">[10]</a></sup>
</p><p>Machine learning programs can perform tasks without being explicitly programmed to do so. It involves computers learning from data provided so that they carry out certain tasks. For simple tasks assigned to computers, it is possible to program algorithms telling the machine how to execute all steps required to solve the problem at hand; on the computer's part, no learning is needed. For more advanced tasks, it can be challenging for a human to manually create the needed algorithms. In practice, it can turn out to be more effective to help the machine develop its own algorithm, rather than having human programmers specify every needed step.<sup><a href="#cite_note-Alpaydin2020-11">[11]</a></sup>
</p><p>The discipline of machine learning employs various approaches to teach computers to accomplish tasks where no fully satisfactory algorithm is available. In cases where vast numbers of potential answers exist, one approach is to label some of the correct answers as valid. This can then be used as training data for the computer to improve the algorithm(s) it uses to determine correct answers. For example, to train a system for the task of digital character recognition, the <a href="/wiki/MNIST_database">MNIST</a> dataset of handwritten digits has often been used.<sup><a href="#cite_note-Alpaydin2020-11">[11]</a></sup>
</p>
<h2>History and relationships to other fields[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=2">edit</a>]</h2>
<p>The term <i>machine learning</i> was coined in 1959 by <a href="/wiki/Arthur_Samuel_(computer_scientist)">Arthur Samuel</a>, an <a href="/wiki/IBM">IBM</a> employee and pioneer in the field of <a href="/wiki/Computer_gaming">computer gaming</a> and <a href="/wiki/Artificial_intelligence">artificial intelligence</a>.<sup><a href="#cite_note-Samuel-12">[12]</a></sup><sup><a href="#cite_note-13">[13]</a></sup> The synonym <i>self-teaching computers</i> was also used in this time period.<sup><a href="#cite_note-cyberthreat-14">[14]</a></sup><sup><a href="#cite_note-15">[15]</a></sup>
</p><p>By the early 1960s an experimental "learning machine" with <a href="/wiki/Punched_tape">punched tape</a> memory, called CyberTron, had been developed by <a href="/wiki/Raytheon_Company">Raytheon Company</a> to analyze sonar signals, electrocardiograms, and speech patterns using rudimentary <a href="/wiki/Reinforcement_learning">reinforcement learning</a>. It was repetitively "trained" by a human operator/teacher to recognize patterns and equipped with a "<a href="/wiki/Goof">goof</a>" button to cause it to re-evaluate incorrect decisions.<sup><a href="#cite_note-16">[16]</a></sup> A representative book on research into machine learning during the 1960s was Nilsson's book on Learning Machines, dealing mostly with machine learning for pattern classification.<sup><a href="#cite_note-17">[17]</a></sup> Interest related to pattern recognition continued into the 1970s, as described by Duda and Hart in 1973.<sup><a href="#cite_note-18">[18]</a></sup> In 1981 a report was given on using teaching strategies so that a <a href="/wiki/Neural_network">neural network</a> learns to recognize 40 characters (26 letters, 10 digits, and 4 special symbols) from a computer terminal.<sup><a href="#cite_note-19">[19]</a></sup>
</p><p><a href="/wiki/Tom_M._Mitchell">Tom M. Mitchell</a> provided a widely quoted, more formal definition of the algorithms studied in the machine learning field: "A computer program is said to learn from experience <i>E</i> with respect to some class of tasks <i>T</i> and performance measure <i>P</i> if its performance at tasks in <i>T</i>, as measured by <i>P</i>, improves with experience <i>E</i>."<sup><a href="#cite_note-Mitchell-1997-20">[20]</a></sup> This definition of the tasks in which machine learning is concerned offers a fundamentally <a href="/wiki/Operational_definition">operational definition</a> rather than defining the field in cognitive terms. This follows <a href="/wiki/Alan_Turing">Alan Turing</a>'s proposal in his paper "<a href="/wiki/Computing_Machinery_and_Intelligence">Computing Machinery and Intelligence</a>", in which the question "Can machines think?" is replaced with the question "Can machines do what we (as thinking entities) can do?".<sup><a href="#cite_note-21">[21]</a></sup>
</p><p>Modern-day machine learning has two objectives, one is to classify data based on models which have been developed, the other purpose is to make predictions for future outcomes based on these models. A hypothetical algorithm specific to classifying data may use computer vision of moles coupled with supervised learning in order to train it to classify the cancerous moles. A machine learning algorithm for stock trading may inform the trader of future potential predictions.<sup><a href="#cite_note-22">[22]</a></sup>
</p>
<h3>Artificial intelligence[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=3">edit</a>]</h3>
<div><p><a href="/wiki/File:AI_hierarchy.svg"></a></p><div><p>Machine learning as subfield of AI<sup><a href="#cite_note-journalimcms.org-23">[23]</a></sup></p></div></div>
<div><p><a href="/wiki/File:Fig-y_Part_of_ML_as_subfield_of_AI_or_AI_as_subfield_of_ML.jpg"></a></p><div><p>Part of machine learning as subfield of AI or part of AI as subfield of machine learning<sup><a href="#cite_note-24">[24]</a></sup></p></div></div>
<p>As a scientific endeavor, machine learning grew out of the quest for artificial intelligence. In the early days of AI as an <a href="/wiki/Discipline_(academia)">academic discipline</a>, some researchers were interested in having machines learn from data. They attempted to approach the problem with various symbolic methods, as well as what was then termed "<a href="/wiki/Neural_network">neural networks</a>"; these were mostly <a href="/wiki/Perceptron">perceptrons</a> and <a href="/wiki/ADALINE">other models</a> that were later found to be reinventions of the <a href="/wiki/Generalized_linear_model">generalized linear models</a> of statistics.<sup><a href="#cite_note-25">[25]</a></sup> <a href="/wiki/Probabilistic_reasoning">Probabilistic reasoning</a> was also employed, especially in <a href="/wiki/Automated_medical_diagnosis">automated medical diagnosis</a>.<sup><a href="#cite_note-aima-26">[26]</a></sup><sup>: 488 </sup>
</p><p>However, an increasing emphasis on the <a href="/wiki/GOFAI">logical, knowledge-based approach</a> caused a rift between AI and machine learning. Probabilistic systems were plagued by theoretical and practical problems of data acquisition and representation.<sup><a href="#cite_note-aima-26">[26]</a></sup><sup>: 488 </sup> By 1980, <a href="/wiki/Expert_system">expert systems</a> had come to dominate AI, and statistics was out of favor.<sup><a href="#cite_note-changing-27">[27]</a></sup> Work on symbolic/knowledge-based learning did continue within AI, leading to <a href="/wiki/Inductive_logic_programming">inductive logic programming</a>, but the more statistical line of research was now outside the field of AI proper, in <a href="/wiki/Pattern_recognition">pattern recognition</a> and <a href="/wiki/Information_retrieval">information retrieval</a>.<sup><a href="#cite_note-aima-26">[26]</a></sup><sup>: 708–710, 755 </sup> Neural networks research had been abandoned by AI and <a href="/wiki/Computer_science">computer science</a> around the same time. This line, too, was continued outside the AI/CS field, as "<a href="/wiki/Connectionism">connectionism</a>", by researchers from other disciplines including <a href="/wiki/John_Hopfield">Hopfield</a>, <a href="/wiki/David_Rumelhart">Rumelhart</a>, and <a href="/wiki/Geoff_Hinton">Hinton</a>. Their main success came in the mid-1980s with the reinvention of <a href="/wiki/Backpropagation">backpropagation</a>.<sup><a href="#cite_note-aima-26">[26]</a></sup><sup>: 25 </sup>
</p><p>Machine learning (ML), reorganized as a separate field, started to flourish in the 1990s. The field changed its goal from achieving artificial intelligence to tackling solvable problems of a practical nature. It shifted focus away from the <a href="/wiki/Symbolic_artificial_intelligence">symbolic approaches</a> it had inherited from AI, and toward methods and models borrowed from statistics, <a href="/wiki/Fuzzy_logic">fuzzy logic</a>, and <a href="/wiki/Probability_theory">probability theory</a>.<sup><a href="#cite_note-changing-27">[27]</a></sup>
</p><p>The difference between ML and AI is frequently misunderstood. ML learns and predicts based on passive observations, whereas AI implies an agent interacting with the environment to learn and take actions that maximize its chance of successfully achieving its goals.<sup><a href="#cite_note-:3-28">[28]</a></sup>
</p><p>As of 2020, many sources continue to assert that ML remains a subfield of AI.<sup><a href="#cite_note-:4-29">[29]</a></sup><sup><a href="#cite_note-islr-30">[30]</a></sup><sup><a href="#cite_note-changing-27">[27]</a></sup> Others have the view that not all ML is part of AI, but only an 'intelligent subset' of ML should be considered AI.<sup><a href="#cite_note-bishop2006-5">[5]</a></sup><sup><a href="#cite_note-:5-31">[31]</a></sup><sup><a href="#cite_note-alpaydin-32">[32]</a></sup>
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<h3>Data mining[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=4">edit</a>]</h3>
<p>Machine learning and <a href="/wiki/Data_mining">data mining</a> often employ the same methods and overlap significantly, but while machine learning focuses on prediction, based on <i>known</i> properties learned from the training data, <a href="/wiki/Data_mining">data mining</a> focuses on the <a href="/wiki/Discovery_(observation)">discovery</a> of (previously) <i>unknown</i> properties in the data (this is the analysis step of <a href="/wiki/Knowledge_discovery">knowledge discovery</a> in databases). Data mining uses many machine learning methods, but with different goals; on the other hand, machine learning also employs data mining methods as "unsupervised learning" or as a preprocessing step to improve learner accuracy. Much of the confusion between these two research communities (which do often have separate conferences and separate journals, <a href="/wiki/ECML_PKDD">ECML PKDD</a> being a major exception) comes from the basic assumptions they work with: in machine learning, performance is usually evaluated with respect to the ability to <i>reproduce known</i> knowledge, while in knowledge discovery and data mining (KDD) the key task is the discovery of previously <i>unknown</i> knowledge. Evaluated with respect to known knowledge, an uninformed (unsupervised) method will easily be outperformed by other supervised methods, while in a typical KDD task, supervised methods cannot be used due to the unavailability of training data.
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<h3>Optimization[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=5">edit</a>]</h3>
<p>Machine learning also has intimate ties to <a href="/wiki/Mathematical_optimization">optimization</a>: many learning problems are formulated as minimization of some <a href="/wiki/Loss_function">loss function</a> on a training set of examples. Loss functions express the discrepancy between the predictions of the model being trained and the actual problem instances (for example, in classification, one wants to assign a label to instances, and models are trained to correctly predict the pre-assigned labels of a set of examples).<sup><a href="#cite_note-33">[33]</a></sup>
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<h3>Generalization[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=6">edit</a>]</h3>
<p>The difference between optimization and machine learning arises from the goal of <a href="/wiki/Generalization_(learning)">generalization</a>: while optimization algorithms can minimize the loss on a training set, machine learning is concerned with minimizing the loss on unseen samples. Characterizing the generalization of various learning algorithms is an active topic of current research, especially for <a href="/wiki/Deep_learning">deep learning</a> algorithms.
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<h3>Statistics[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=7">edit</a>]</h3>
<p>Machine learning and <a href="/wiki/Statistics">statistics</a> are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population <a href="/wiki/Statistical_inference">inferences</a> from a <a href="/wiki/Sample_(statistics)">sample</a>, while machine learning finds generalizable predictive patterns.<sup><a href="#cite_note-34">[34]</a></sup> According to <a href="/wiki/Michael_I._Jordan">Michael I. Jordan</a>, the ideas of machine learning, from methodological principles to theoretical tools, have had a long pre-history in statistics.<sup><a href="#cite_note-mi_jordan_ama-35">[35]</a></sup> He also suggested the term <a href="/wiki/Data_science">data science</a> as a placeholder to call the overall field.<sup><a href="#cite_note-mi_jordan_ama-35">[35]</a></sup>
</p><p><a href="/wiki/Leo_Breiman">Leo Breiman</a> distinguished two statistical modeling paradigms: data model and algorithmic model,<sup><a href="#cite_note-:4-29">[29]</a></sup> wherein "algorithmic model" means more or less the machine learning algorithms like <a href="/wiki/Random_forest">Random Forest</a>.
</p><p>Some statisticians have adopted methods from machine learning, leading to a combined field that they call <i>statistical learning</i>.<sup><a href="#cite_note-islr-30">[30]</a></sup>
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<h3>Physics[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=8">edit</a>]</h3>
<p>Analytical and computational techniques derived from statistical physics of disordered systems, can be extended to large-scale problems, including machine learning, e.g., to analyze the weight space of deep <a href="/wiki/Neural_networks">neural networks</a>.<sup><a href="#cite_note-36">[36]</a></sup> Statistical physics is thus finding applications in the area of <a href="/wiki/Medical_diagnostics">medical diagnostics</a>.<sup><a href="#cite_note-37">[37]</a></sup>
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<h2> Theory[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=9">edit</a>]</h2>
<p>A core objective of a learner is to generalize from its experience.<sup><a href="#cite_note-bishop2006-5">[5]</a></sup><sup><a href="#cite_note-:5-31">[31]</a></sup> Generalization in this context is the ability of a learning machine to perform accurately on new, unseen examples/tasks after having experienced a learning data set. The training examples come from some generally unknown probability distribution (considered representative of the space of occurrences) and the learner has to build a general model about this space that enables it to produce sufficiently accurate predictions in new cases.
</p><p>The computational analysis of machine learning algorithms and their performance is a branch of <a href="/wiki/Theoretical_computer_science">theoretical computer science</a> known as <a href="/wiki/Computational_learning_theory">computational learning theory</a> via the <a href="/wiki/Probably_approximately_correct_learning">Probably Approximately Correct Learning</a> (PAC) model. Because training sets are finite and the future is uncertain, learning theory usually does not yield guarantees of the performance of algorithms. Instead, probabilistic bounds on the performance are quite common. The <a href="/wiki/Bias%E2%80%93variance_decomposition">bias–variance decomposition</a> is one way to quantify generalization <a href="/wiki/Errors_and_residuals">error</a>.
</p><p>For the best performance in the context of generalization, the complexity of the hypothesis should match the complexity of the function underlying the data. If the hypothesis is less complex than the function, then the model has under fitted the data. If the complexity of the model is increased in response, then the training error decreases. But if the hypothesis is too complex, then the model is subject to <a href="/wiki/Overfitting">overfitting</a> and generalization will be poorer.<sup><a href="#cite_note-alpaydin-32">[32]</a></sup>
</p><p>In addition to performance bounds, learning theorists study the time complexity and feasibility of learning. In computational learning theory, a computation is considered feasible if it can be done in <a href="/wiki/Time_complexity#Polynomial_time">polynomial time</a>. There are two kinds of <a href="/wiki/Time_complexity">time complexity</a> results: Positive results show that a certain class of functions can be learned in polynomial time. Negative results show that certain classes cannot be learned in polynomial time.
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<h2>Approaches[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=10">edit</a>]</h2>
<p>
Machine learning approaches are traditionally divided into three broad categories, which correspond to learning paradigms, depending on the nature of the "signal" or "feedback" available to the learning system:
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<ul><li><a href="/wiki/Supervised_learning">Supervised learning</a>: The computer is presented with example inputs and their desired outputs, given by a "teacher", and the goal is to learn a general rule that <a href="/wiki/Map_(mathematics)">maps</a> inputs to outputs.</li>
<li><a href="/wiki/Unsupervised_learning">Unsupervised learning</a>: No labels are given to the learning algorithm, leaving it on its own to find structure in its input. Unsupervised learning can be a goal in itself (discovering hidden patterns in data) or a means towards an end (<a href="/wiki/Feature_learning">feature learning</a>).</li>
<li><a href="/wiki/Reinforcement_learning">Reinforcement learning</a>: A computer program interacts with a dynamic environment in which it must perform a certain goal (such as <a href="/wiki/Autonomous_car">driving a vehicle</a> or playing a game against an opponent). As it navigates its problem space, the program is provided feedback that's analogous to rewards, which it tries to maximize.<sup><a href="#cite_note-bishop2006-5">[5]</a></sup></li></ul>
<h3>Supervised learning[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=11">edit</a>]</h3>
<div><p><a href="/wiki/File:Svm_max_sep_hyperplane_with_margin.png"></a></p><div><p>A <a href="/wiki/Support-vector_machine">support-vector machine</a> is a supervised learning model that divides the data into regions separated by a <a href="/wiki/Linear_classifier">linear boundary</a>. Here, the linear boundary divides the black circles from the white.</p></div></div>
<p>Supervised learning algorithms build a mathematical model of a set of data that contains both the inputs and the desired outputs.<sup><a href="#cite_note-38">[38]</a></sup> The data is known as <a href="/wiki/Training_data">training data</a>, and consists of a set of training examples. Each training example has one or more inputs and the desired output, also known as a supervisory signal. In the mathematical model, each training example is represented by an <a href="/wiki/Array_data_structure">array</a> or vector, sometimes called a feature vector, and the training data is represented by a <a href="/wiki/Matrix_(mathematics)">matrix</a>. Through <a href="/wiki/Mathematical_optimization#Computational_optimization_techniques">iterative optimization</a> of an <a href="/wiki/Loss_function">objective function</a>, supervised learning algorithms learn a function that can be used to predict the output associated with new inputs.<sup><a href="#cite_note-39">[39]</a></sup> An optimal function will allow the algorithm to correctly determine the output for inputs that were not a part of the training data. An algorithm that improves the accuracy of its outputs or predictions over time is said to have learned to perform that task.<sup><a href="#cite_note-Mitchell-1997-20">[20]</a></sup>
</p><p>Types of supervised-learning algorithms include <a href="/wiki/Active_learning_(machine_learning)">active learning</a>, <a href="/wiki/Statistical_classification">classification</a> and <a href="/wiki/Regression_analysis">regression</a>.<sup><a href="#cite_note-:3-28">[28]</a></sup> Classification algorithms are used when the outputs are restricted to a limited set of values, and regression algorithms are used when the outputs may have any numerical value within a range. As an example, for a classification algorithm that filters emails, the input would be an incoming email, and the output would be the name of the folder in which to file the email.
</p><p><a href="/wiki/Similarity_learning">Similarity learning</a> is an area of supervised machine learning closely related to regression and classification, but the goal is to learn from examples using a similarity function that measures how similar or related two objects are. It has applications in <a href="/wiki/Ranking">ranking</a>, <a href="/wiki/Recommender_system">recommendation systems</a>, visual identity tracking, face verification, and speaker verification.
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<h3>Unsupervised learning[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=12">edit</a>]</h3>
<p>Unsupervised learning algorithms take a set of data that contains only inputs, and find structure in the data, like grouping or clustering of data points. The algorithms, therefore, learn from test data that has not been labeled, classified or categorized. Instead of responding to feedback, unsupervised learning algorithms identify commonalities in the data and react based on the presence or absence of such commonalities in each new piece of data. A central application of unsupervised learning is in the field of <a href="/wiki/Density_estimation">density estimation</a> in <a href="/wiki/Statistics">statistics</a>, such as finding the <a href="/wiki/Probability_density_function">probability density function</a>.<sup><a href="#cite_note-JordanBishop2004-40">[40]</a></sup> Though unsupervised learning encompasses other domains involving summarizing and explaining data features.
</p><p>Cluster analysis is the assignment of a set of observations into subsets (called <i>clusters</i>) so that observations within the same cluster are similar according to one or more predesignated criteria, while observations drawn from different clusters are dissimilar. Different clustering techniques make different assumptions on the structure of the data, often defined by some <i>similarity metric</i> and evaluated, for example, by <i>internal compactness</i>, or the similarity between members of the same cluster, and <i>separation</i>, the difference between clusters. Other methods are based on <i>estimated density</i> and <i>graph connectivity</i>.
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<h3>Semi-supervised learning[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=13">edit</a>]</h3>
<p>Semi-supervised learning falls between <a href="/wiki/Unsupervised_learning">unsupervised learning</a> (without any labeled training data) and <a href="/wiki/Supervised_learning">supervised learning</a> (with completely labeled training data). Some of the training examples are missing training labels, yet many machine-learning researchers have found that unlabeled data, when used in conjunction with a small amount of labeled data, can produce a considerable improvement in learning accuracy.
</p><p>In <a href="/wiki/Weak_supervision">weakly supervised learning</a>, the training labels are noisy, limited, or imprecise; however, these labels are often cheaper to obtain, resulting in larger effective training sets.<sup><a href="#cite_note-41">[41]</a></sup>
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<h3>Reinforcement learning[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=14">edit</a>]</h3>
<p>Reinforcement learning is an area of machine learning concerned with how <a href="/wiki/Software_agent">software agents</a> ought to take <a href="/wiki/Action_selection">actions</a> in an environment so as to maximize some notion of cumulative reward. Due to its generality, the field is studied in many other disciplines, such as <a href="/wiki/Game_theory">game theory</a>, <a href="/wiki/Control_theory">control theory</a>, <a href="/wiki/Operations_research">operations research</a>, <a href="/wiki/Information_theory">information theory</a>, <a href="/wiki/Simulation-based_optimization">simulation-based optimization</a>, <a href="/wiki/Multi-agent_system">multi-agent systems</a>, <a href="/wiki/Swarm_intelligence">swarm intelligence</a>, <a href="/wiki/Statistics">statistics</a> and <a href="/wiki/Genetic_algorithm">genetic algorithms</a>. In machine learning, the environment is typically represented as a <a href="/wiki/Markov_decision_process">Markov decision process</a> (MDP). Many reinforcements learning algorithms use <a href="/wiki/Dynamic_programming">dynamic programming</a> techniques.<sup><a href="#cite_note-42">[42]</a></sup> Reinforcement learning algorithms do not assume knowledge of an exact mathematical model of the MDP and are used when exact models are infeasible. Reinforcement learning algorithms are used in autonomous vehicles or in learning to play a game against a human opponent.
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<h3>Dimensionality reduction[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=15">edit</a>]</h3>
<p>Dimensionality reduction is a process of reducing the number of random variables under consideration by obtaining a set of principal variables.<sup><a href="#cite_note-43">[43]</a></sup> In other words, it is a process of reducing the dimension of the feature set, also called the "number of features". Most of the dimensionality reduction techniques can be considered as either feature elimination or extraction. One of the popular methods of dimensionality reduction is <a href="/wiki/Principal_component_analysis">principal component analysis</a> (PCA). PCA involves changing higher-dimensional data (e.g., 3D) to a smaller space (e.g., 2D). This results in a smaller dimension of data (2D instead of 3D), while keeping all original variables in the model without changing the data.<sup><a href="#cite_note-44">[44]</a></sup>
The <a href="/wiki/Manifold_hypothesis">manifold hypothesis</a> proposes that high-dimensional data sets lie along low-dimensional <a href="/wiki/Manifold">manifolds</a>, and many dimensionality reduction techniques make this assumption, leading to the area of <a href="/wiki/Manifold_learning">manifold learning</a> and <a href="/wiki/Manifold_regularization">manifold regularization</a>.
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<h3>Other types[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=16">edit</a>]</h3>
<p>Other approaches have been developed which don't fit neatly into this three-fold categorization, and sometimes more than one is used by the same machine learning system. For example, <a href="/wiki/Topic_modeling">topic modeling</a>, <a href="/wiki/Meta-learning_(computer_science)">meta-learning</a>.<sup><a href="#cite_note-45">[45]</a></sup>
</p><p>As of 2022, <a href="/wiki/Deep_learning">deep learning</a> is the dominant approach for much ongoing work in the field of machine learning.<sup><a href="#cite_note-Alpaydin2020-11">[11]</a></sup>
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<h4>Self-learning[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=17">edit</a>]</h4>
<p>Self-learning, as a machine learning paradigm was introduced in 1982 along with a neural network capable of self-learning, named <i>crossbar adaptive array</i> (CAA).<sup><a href="#cite_note-46">[46]</a></sup> It is learning with no external rewards and no external teacher advice. The CAA self-learning algorithm computes, in a crossbar fashion, both decisions about actions and emotions (feelings) about consequence situations. The system is driven by the interaction between cognition and emotion.<sup><a href="#cite_note-47">[47]</a></sup>
The self-learning algorithm updates a memory matrix W =||w(a,s)|| such that in each iteration executes the following machine learning routine: 
</p>
<ol><li>in situation <i>s</i> perform action <i>a</i></li>
<li>receive consequence situation <i>s'</i></li>
<li>compute emotion of being in consequence situation <i>v(s')</i></li>
<li>update crossbar memory <i>w'(a,s) = w(a,s) + v(s')</i></li></ol>
<p>It is a system with only one input, situation, and only one output, action (or behavior) a. There is neither a separate reinforcement input nor an advice input from the environment. The backpropagated value (secondary reinforcement) is the emotion toward the consequence situation. The CAA exists in two environments, one is the behavioral environment where it behaves, and the other is the genetic environment, wherefrom it initially and only once receives initial emotions about situations to be encountered in the behavioral environment. After receiving the genome (species) vector from the genetic environment, the CAA learns a goal-seeking behavior, in an environment that contains both desirable and undesirable situations.<sup><a href="#cite_note-48">[48]</a></sup>
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<h4>Feature learning[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=18">edit</a>]</h4>
<p>Several learning algorithms aim at discovering better representations of the inputs provided during training.<sup><a href="#cite_note-pami-49">[49]</a></sup> Classic examples include <a href="/wiki/Principal_component_analysis">principal component analysis</a> and cluster analysis. Feature learning algorithms, also called representation learning algorithms, often attempt to preserve the information in their input but also transform it in a way that makes it useful, often as a pre-processing step before performing classification or predictions. This technique allows reconstruction of the inputs coming from the unknown data-generating distribution, while not being necessarily faithful to configurations that are implausible under that distribution. This replaces manual <a href="/wiki/Feature_engineering">feature engineering</a>, and allows a machine to both learn the features and use them to perform a specific task.
</p><p>Feature learning can be either supervised or unsupervised. In supervised feature learning, features are learned using labeled input data. Examples include <a href="/wiki/Artificial_neural_network">artificial neural networks</a>, <a href="/wiki/Multilayer_perceptron">multilayer perceptrons</a>, and supervised <a href="/wiki/Dictionary_learning">dictionary learning</a>. In unsupervised feature learning, features are learned with unlabeled input data. Examples include dictionary learning, <a href="/wiki/Independent_component_analysis">independent component analysis</a>, <a href="/wiki/Autoencoder">autoencoders</a>, <a href="/wiki/Matrix_decomposition">matrix factorization</a><sup><a href="#cite_note-50">[50]</a></sup> and various forms of <a href="/wiki/Cluster_analysis">clustering</a>.<sup><a href="#cite_note-coates2011-51">[51]</a></sup><sup><a href="#cite_note-52">[52]</a></sup><sup><a href="#cite_note-jurafsky-53">[53]</a></sup>
</p><p><a href="/wiki/Manifold_learning">Manifold learning</a> algorithms attempt to do so under the constraint that the learned representation is low-dimensional. <a href="/wiki/Sparse_coding">Sparse coding</a> algorithms attempt to do so under the constraint that the learned representation is sparse, meaning that the mathematical model has many zeros. <a href="/wiki/Multilinear_subspace_learning">Multilinear subspace learning</a> algorithms aim to learn low-dimensional representations directly from <a href="/wiki/Tensor">tensor</a> representations for multidimensional data, without reshaping them into higher-dimensional vectors.<sup><a href="#cite_note-54">[54]</a></sup> <a href="/wiki/Deep_learning">Deep learning</a> algorithms discover multiple levels of representation, or a hierarchy of features, with higher-level, more abstract features defined in terms of (or generating) lower-level features. It has been argued that an intelligent machine is one that learns a representation that disentangles the underlying factors of variation that explain the observed data.<sup><a href="#cite_note-55">[55]</a></sup>
</p><p>Feature learning is motivated by the fact that machine learning tasks such as classification often require input that is mathematically and computationally convenient to process. However, real-world data such as images, video, and sensory data has not yielded attempts to algorithmically define specific features. An alternative is to discover such features or representations through examination, without relying on explicit algorithms.
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<h4>Sparse dictionary learning[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=19">edit</a>]</h4>
<p>Sparse dictionary learning is a feature learning method where a training example is represented as a linear combination of <a href="/wiki/Basis_function">basis functions</a>, and is assumed to be a <a href="/wiki/Sparse_matrix">sparse matrix</a>. The method is <a href="/wiki/Strongly_NP-hard">strongly NP-hard</a> and difficult to solve approximately.<sup><a href="#cite_note-56">[56]</a></sup> A popular <a href="/wiki/Heuristic">heuristic</a> method for sparse dictionary learning is the <a href="/wiki/K-SVD">K-SVD</a> algorithm. Sparse dictionary learning has been applied in several contexts. In classification, the problem is to determine the class to which a previously unseen training example belongs. For a dictionary where each class has already been built, a new training example is associated with the class that is best sparsely represented by the corresponding dictionary. Sparse dictionary learning has also been applied in <a href="/wiki/Image_de-noising">image de-noising</a>. The key idea is that a clean image patch can be sparsely represented by an image dictionary, but the noise cannot.<sup><a href="#cite_note-57">[57]</a></sup>
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<h4>Anomaly detection[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=20">edit</a>]</h4>
<p>In <a href="/wiki/Data_mining">data mining</a>, anomaly detection, also known as outlier detection, is the identification of rare items, events or observations which raise suspicions by differing significantly from the majority of the data.<sup><a href="#cite_note-:0-58">[58]</a></sup> Typically, the anomalous items represent an issue such as <a href="/wiki/Bank_fraud">bank fraud</a>, a structural defect, medical problems or errors in a text. Anomalies are referred to as <a href="/wiki/Outlier">outliers</a>, novelties, noise, deviations and exceptions.<sup><a href="#cite_note-59">[59]</a></sup>
</p><p>In particular, in the context of abuse and network intrusion detection, the interesting objects are often not rare objects, but unexpected bursts of inactivity. This pattern does not adhere to the common statistical definition of an outlier as a rare object. Many outlier detection methods (in particular, unsupervised algorithms) will fail on such data unless aggregated appropriately. Instead, a cluster analysis algorithm may be able to detect the micro-clusters formed by these patterns.<sup><a href="#cite_note-60">[60]</a></sup>
</p><p>Three broad categories of anomaly detection techniques exist.<sup><a href="#cite_note-ChandolaSurvey-61">[61]</a></sup> Unsupervised anomaly detection techniques detect anomalies in an unlabeled test data set under the assumption that the majority of the instances in the data set are normal, by looking for instances that seem to fit the least to the remainder of the data set. Supervised anomaly detection techniques require a data set that has been labeled as "normal" and "abnormal" and involves training a classifier (the key difference to many other statistical classification problems is the inherently unbalanced nature of outlier detection). Semi-supervised anomaly detection techniques construct a model representing normal behavior from a given normal training data set and then test the likelihood of a test instance to be generated by the model.
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<h4>Robot learning[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=21">edit</a>]</h4>
<p><a href="/wiki/Robot_learning">Robot learning</a> is inspired by a multitude of machine learning methods, starting from supervised learning, reinforcement learning,<sup><a href="#cite_note-62">[62]</a></sup><sup><a href="#cite_note-63">[63]</a></sup> and finally <a href="/wiki/Meta-learning_(computer_science)">meta-learning</a> (e.g. MAML).
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<h4>Association rules[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=22">edit</a>]</h4>
<p>Association rule learning is a <a href="/wiki/Rule-based_machine_learning">rule-based machine learning</a> method for discovering relationships between variables in large databases. It is intended to identify strong rules discovered in databases using some measure of "interestingness".<sup><a href="#cite_note-piatetsky-64">[64]</a></sup>
</p><p>Rule-based machine learning is a general term for any machine learning method that identifies, learns, or evolves "rules" to store, manipulate or apply knowledge. The defining characteristic of a rule-based machine learning algorithm is the identification and utilization of a set of relational rules that collectively represent the knowledge captured by the system. This is in contrast to other machine learning algorithms that commonly identify a singular model that can be universally applied to any instance in order to make a prediction.<sup><a href="#cite_note-65">[65]</a></sup> Rule-based machine learning approaches include <a href="/wiki/Learning_classifier_system">learning classifier systems</a>, association rule learning, and <a href="/wiki/Artificial_immune_system">artificial immune systems</a>.
</p><p>Based on the concept of strong rules, <a href="/wiki/Rakesh_Agrawal_(computer_scientist)">Rakesh Agrawal</a>, <a href="/wiki/Tomasz_Imieli%C5%84ski">Tomasz Imieliński</a> and Arun Swami introduced association rules for discovering regularities between products in large-scale transaction data recorded by <a href="/wiki/Point-of-sale">point-of-sale</a> (POS) systems in supermarkets.<sup><a href="#cite_note-mining-66">[66]</a></sup> For example, the rule found in the sales data of a supermarket would indicate that if a customer buys onions and potatoes together, they are likely to also buy hamburger meat. Such information can be used as the basis for decisions about marketing activities such as promotional <a href="/wiki/Pricing">pricing</a> or <a href="/wiki/Product_placement">product placements</a>. In addition to <a href="/wiki/Market_basket_analysis">market basket analysis</a>, association rules are employed today in application areas including <a href="/wiki/Web_usage_mining">Web usage mining</a>, <a href="/wiki/Intrusion_detection">intrusion detection</a>, <a href="/wiki/Continuous_production">continuous production</a>, and <a href="/wiki/Bioinformatics">bioinformatics</a>. In contrast with <a href="/wiki/Sequence_mining">sequence mining</a>, association rule learning typically does not consider the order of items either within a transaction or across transactions.
</p><p>Learning classifier systems (LCS) are a family of rule-based machine learning algorithms that combine a discovery component, typically a <a href="/wiki/Genetic_algorithm">genetic algorithm</a>, with a learning component, performing either <a href="/wiki/Supervised_learning">supervised learning</a>, <a href="/wiki/Reinforcement_learning">reinforcement learning</a>, or <a href="/wiki/Unsupervised_learning">unsupervised learning</a>. They seek to identify a set of context-dependent rules that collectively store and apply knowledge in a <a href="/wiki/Piecewise">piecewise</a> manner in order to make predictions.<sup><a href="#cite_note-67">[67]</a></sup>
</p><p>Inductive logic programming (ILP) is an approach to rule learning using <a href="/wiki/Logic_programming">logic programming</a> as a uniform representation for input examples, background knowledge, and hypotheses. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesized logic program that <a href="/wiki/Entailment">entails</a> all positive and no negative examples. <a href="/wiki/Inductive_programming">Inductive programming</a> is a related field that considers any kind of programming language for representing hypotheses (and not only logic programming), such as <a href="/wiki/Functional_programming">functional programs</a>.
</p><p>Inductive logic programming is particularly useful in <a href="/wiki/Bioinformatics">bioinformatics</a> and <a href="/wiki/Natural_language_processing">natural language processing</a>. <a href="/wiki/Gordon_Plotkin">Gordon Plotkin</a> and <a href="/wiki/Ehud_Shapiro">Ehud Shapiro</a> laid the initial theoretical foundation for inductive machine learning in a logical setting.<sup><a href="#cite_note-68">[68]</a></sup><sup><a href="#cite_note-69">[69]</a></sup><sup><a href="#cite_note-70">[70]</a></sup> Shapiro built their first implementation (Model Inference System) in 1981: a Prolog program that inductively inferred logic programs from positive and negative examples.<sup><a href="#cite_note-71">[71]</a></sup> The term <i>inductive</i> here refers to <a href="/wiki/Inductive_reasoning">philosophical</a> induction, suggesting a theory to explain observed facts, rather than <a href="/wiki/Mathematical_induction">mathematical induction</a>, proving a property for all members of a well-ordered set.
</p>
<h3>Models[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=23">edit</a>]</h3>
<p>Performing machine learning involves creating a <a href="/wiki/Statistical_model">model</a>, which is trained on some training data and then can process additional data to make predictions. Various types of models have been used and researched for machine learning systems.
</p>
<h4>Artificial neural networks[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=24">edit</a>]</h4>
<div><p><a href="/wiki/File:Colored_neural_network.svg"></a></p><div><p>An artificial neural network is an interconnected group of nodes, akin to the vast network of <a href="/wiki/Neuron">neurons</a> in a <a href="/wiki/Brain">brain</a>. Here, each circular node represents an <a href="/wiki/Artificial_neuron">artificial neuron</a> and an arrow represents a connection from the output of one artificial neuron to the input of another.</p></div></div>
<p>Artificial neural networks (ANNs), or <a href="/wiki/Connectionism">connectionist</a> systems, are computing systems vaguely inspired by the <a href="/wiki/Biological_neural_network">biological neural networks</a> that constitute animal <a href="/wiki/Brain">brains</a>. Such systems "learn" to perform tasks by considering examples, generally without being programmed with any task-specific rules.
</p><p>An ANN is a model based on a collection of connected units or nodes called "<a href="/wiki/Artificial_neuron">artificial neurons</a>", which loosely model the <a href="/wiki/Neuron">neurons</a> in a biological <a href="/wiki/Brain">brain</a>. Each connection, like the <a href="/wiki/Synapse">synapses</a> in a biological <a href="/wiki/Brain">brain</a>, can transmit information, a "signal", from one artificial neuron to another. An artificial neuron that receives a signal can process it and then signal additional artificial neurons connected to it. In common ANN implementations, the signal at a connection between artificial neurons is a <a href="/wiki/Real_number">real number</a>, and the output of each artificial neuron is computed by some non-linear function of the sum of its inputs. The connections between artificial neurons are called "edges". Artificial neurons and edges typically have a <a href="/wiki/Weight_(mathematics)">weight</a> that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Artificial neurons may have a threshold such that the signal is only sent if the aggregate signal crosses that threshold. Typically, artificial neurons are aggregated into layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first layer (the input layer) to the last layer (the output layer), possibly after traversing the layers multiple times.
</p><p>The original goal of the ANN approach was to solve problems in the same way that a <a href="/wiki/Human_brain">human brain</a> would. However, over time, attention moved to performing specific tasks, leading to deviations from <a href="/wiki/Biology">biology</a>. Artificial neural networks have been used on a variety of tasks, including <a href="/wiki/Computer_vision">computer vision</a>, <a href="/wiki/Speech_recognition">speech recognition</a>, <a href="/wiki/Machine_translation">machine translation</a>, <a href="/wiki/Social_network">social network</a> filtering, <a href="/wiki/General_game_playing">playing board and video games</a> and <a href="/wiki/Medical_diagnosis">medical diagnosis</a>.
</p><p><a href="/wiki/Deep_learning">Deep learning</a> consists of multiple hidden layers in an artificial neural network. This approach tries to model the way the human brain processes light and sound into vision and hearing. Some successful applications of deep learning are <a href="/wiki/Computer_vision">computer vision</a> and <a href="/wiki/Speech_recognition">speech recognition</a>.<sup><a href="#cite_note-72">[72]</a></sup>
</p>
<h4>Decision trees[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=25">edit</a>]</h4>
<div><p><a href="/wiki/File:Decision_Tree.jpg"></a></p><div><p>A decision tree showing survival probability of passengers on the <a href="/wiki/Titanic">Titanic</a></p></div></div>
<p>Decision tree learning uses a <a href="/wiki/Decision_tree">decision tree</a> as a <a href="/wiki/Predictive_modeling">predictive model</a> to go from observations about an item (represented in the branches) to conclusions about the item's target value (represented in the leaves). It is one of the predictive modeling approaches used in statistics, data mining, and machine learning. Tree models where the target variable can take a discrete set of values are called classification trees; in these tree structures, <a href="/wiki/Leaf_node">leaves</a> represent class labels, and branches represent <a href="/wiki/Logical_conjunction">conjunctions</a> of features that lead to those class labels. Decision trees where the target variable can take continuous values (typically <a href="/wiki/Real_numbers">real numbers</a>) are called regression trees. In decision analysis, a decision tree can be used to visually and explicitly represent decisions and <a href="/wiki/Decision_making">decision making</a>. In data mining, a decision tree describes data, but the resulting classification tree can be an input for decision-making.
</p>
<h4>Support-vector machines[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=26">edit</a>]</h4>
<p>Support-vector machines (SVMs), also known as support-vector networks, are a set of related <a href="/wiki/Supervised_learning">supervised learning</a> methods used for classification and regression. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that predicts whether a new example falls into one category.<sup><a href="#cite_note-CorinnaCortes-73">[73]</a></sup> An SVM training algorithm is a non-<a href="/wiki/Probabilistic_classification">probabilistic</a>, <a href="/wiki/Binary_classifier">binary</a>, <a href="/wiki/Linear_classifier">linear classifier</a>, although methods such as <a href="/wiki/Platt_scaling">Platt scaling</a> exist to use SVM in a probabilistic classification setting. In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the <a href="/wiki/Kernel_trick">kernel trick</a>, implicitly mapping their inputs into high-dimensional feature spaces.
</p>
<h4>Regression analysis[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=27">edit</a>]</h4>
<div><p><a href="/wiki/File:Linear_regression.svg"></a></p><div><p>Illustration of linear regression on a data set</p></div></div>
<p>Regression analysis encompasses a large variety of statistical methods to estimate the relationship between input variables and their associated features. Its most common form is <a href="/wiki/Linear_regression">linear regression</a>, where a single line is drawn to best fit the given data according to a mathematical criterion such as <a href="/wiki/Ordinary_least_squares">ordinary least squares</a>. The latter is often extended by <a href="/wiki/Regularization_(mathematics)">regularization</a> methods to mitigate overfitting and bias, as in <a href="/wiki/Ridge_regression">ridge regression</a>. When dealing with non-linear problems, go-to models include <a href="/wiki/Polynomial_regression">polynomial regression</a> (for example, used for trendline fitting in Microsoft Excel<sup><a href="#cite_note-74">[74]</a></sup>), <a href="/wiki/Logistic_regression">logistic regression</a> (often used in <a href="/wiki/Statistical_classification">statistical classification</a>) or even <a href="/wiki/Kernel_regression">kernel regression</a>, which introduces non-linearity by taking advantage of the <a href="/wiki/Kernel_trick">kernel trick</a> to implicitly map input variables to higher-dimensional space.
</p>
<h4>Bayesian networks[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=28">edit</a>]</h4>
<div><p><a href="/wiki/File:SimpleBayesNetNodes.svg"></a></p><div><p>A simple Bayesian network. Rain influences whether the sprinkler is activated, and both rain and the sprinkler influence whether the grass is wet.</p></div></div>
<p>A Bayesian network, belief network, or directed acyclic graphical model is a probabilistic <a href="/wiki/Graphical_model">graphical model</a> that represents a set of <a href="/wiki/Random_variables">random variables</a> and their <a href="/wiki/Conditional_independence">conditional independence</a> with a <a href="/wiki/Directed_acyclic_graph">directed acyclic graph</a> (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms exist that perform <a href="/wiki/Inference">inference</a> and learning. Bayesian networks that model sequences of variables, like <a href="/wiki/Speech_recognition">speech signals</a> or <a href="/wiki/Peptide_sequence">protein sequences</a>, are called <a href="/wiki/Dynamic_Bayesian_network">dynamic Bayesian networks</a>. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty are called <a href="/wiki/Influence_diagram">influence diagrams</a>.
</p>
<h4>Gaussian processes[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=29">edit</a>]</h4>
<div><p><a href="/wiki/File:Regressions_sine_demo.svg"></a></p><div><p>An example of Gaussian Process Regression (prediction) compared with other regression models<sup><a href="#cite_note-75">[75]</a></sup></p></div></div>
<p>A Gaussian process is a <a href="/wiki/Stochastic_process">stochastic process</a> in which every finite collection of the random variables in the process has a <a href="/wiki/Multivariate_normal_distribution">multivariate normal distribution</a>, and it relies on a pre-defined <a href="/wiki/Covariance_function">covariance function</a>, or kernel, that models how pairs of points relate to each other depending on their locations.
</p><p>Given a set of observed points, or input–output examples, the distribution of the (unobserved) output of a new point as function of its input data, can be directly computed by looking like the observed points and the covariances between those points and the new, unobserved point.
</p><p>Gaussian processes are popular surrogate models in <a href="/wiki/Bayesian_optimization">Bayesian optimization</a> used to do <a href="/wiki/Hyperparameter_optimization">hyperparameter optimization</a>.
</p>
<h4>Genetic algorithms[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=30">edit</a>]</h4>
<p>A genetic algorithm (GA) is a <a href="/wiki/Search_algorithm">search algorithm</a> and <a href="/wiki/Heuristic_(computer_science)">heuristic</a> technique that mimics the process of <a href="/wiki/Natural_selection">natural selection</a>, using methods such as <a href="/wiki/Mutation_(genetic_algorithm)">mutation</a> and <a href="/wiki/Crossover_(genetic_algorithm)">crossover</a> to generate new <a href="/wiki/Chromosome_(genetic_algorithm)">genotypes</a> in the hope of finding good solutions to a given problem. In machine learning, genetic algorithms were used in the 1980s and 1990s.<sup><a href="#cite_note-76">[76]</a></sup><sup><a href="#cite_note-77">[77]</a></sup> Conversely, machine learning techniques have been used to improve the performance of genetic and <a href="/wiki/Evolutionary_algorithm">evolutionary algorithms</a>.<sup><a href="#cite_note-78">[78]</a></sup>
</p>
<h3>Training models[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=31">edit</a>]</h3>
<p>Typically, machine learning models require a high quantity of reliable data in order for the models to perform accurate predictions. When training a machine learning model, machine learning engineers need to target and collect a large and representative sample of data. Data from the training set can be as varied as a corpus of text, a collection of images, sensor data, and data collected from individual users of a service. <a href="/wiki/Overfitting">Overfitting</a> is something to watch out for when training a machine learning model. Trained models derived from biased or non-evaluated data can result in skewed or undesired predictions. Bias models may result in detrimental outcomes thereby furthering the negative impacts on society or objectives. <a href="/wiki/Algorithmic_bias">Algorithmic bias</a> is a potential result of data not being fully prepared for training. Machine learning ethics is becoming a field of study and notably be integrated within machine learning engineering teams.
</p>
<h4>Federated learning[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=32">edit</a>]</h4>
<p>Federated learning is an adapted form of <a href="/wiki/Distributed_artificial_intelligence">distributed artificial intelligence</a> to training machine learning models that decentralizes the training process, allowing for users' privacy to be maintained by not needing to send their data to a centralized server. This also increases efficiency by decentralizing the training process to many devices. For example, <a href="/wiki/Gboard">Gboard</a> uses federated machine learning to train search query prediction models on users' mobile phones without having to send individual searches back to <a href="/wiki/Google">Google</a>.<sup><a href="#cite_note-79">[79]</a></sup>
</p>
<h2>Applications[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=33">edit</a>]</h2>
<p>There are many applications for machine learning, including:
</p>
<div>
<ul><li><a href="/wiki/Precision_agriculture">Agriculture</a></li>
<li><a href="/wiki/Computational_anatomy">Anatomy</a></li>
<li><a href="/wiki/Adaptive_website">Adaptive website</a></li>
<li><a href="/wiki/Affective_computing">Affective computing</a></li>
<li><a href="/wiki/Astroinformatics">Astronomy</a></li>
<li><a href="/wiki/Automated_decision-making">Automated decision-making</a></li>
<li><a href="/wiki/Banking">Banking</a></li>
<li><a href="/wiki/Behaviorism">Behaviorism</a></li>
<li><a href="/wiki/Bioinformatics">Bioinformatics</a></li>
<li><a href="/wiki/Brain%E2%80%93computer_interface">Brain–machine interfaces</a></li>
<li><a href="/wiki/Cheminformatics">Cheminformatics</a></li>
<li><a href="/wiki/Citizen_Science">Citizen Science</a></li>
<li><a href="/wiki/Climate_Science">Climate Science</a></li>
<li><a href="/wiki/Network_simulation">Computer networks</a></li>
<li><a href="/wiki/Computer_vision">Computer vision</a></li>
<li><a href="/wiki/Credit-card_fraud">Credit-card fraud</a> detection</li>
<li><a href="/wiki/Data_quality">Data quality</a></li>
<li><a href="/wiki/DNA_sequence">DNA sequence</a> classification</li>
<li><a href="/wiki/Computational_economics">Economics</a></li>
<li><a href="/wiki/Financial_market">Financial market</a> analysis<sup><a href="#cite_note-80">[80]</a></sup></li>
<li><a href="/wiki/General_game_playing">General game playing</a></li>
<li><a href="/wiki/Handwriting_recognition">Handwriting recognition</a></li>
<li><a href="/wiki/Information_retrieval">Information retrieval</a></li>
<li><a href="/wiki/Insurance">Insurance</a></li>
<li><a href="/wiki/Internet_fraud">Internet fraud</a> detection</li>
<li><a href="/wiki/Knowledge_graph_embedding">Knowledge graph embedding</a></li>
<li><a href="/wiki/Computational_linguistics">Linguistics</a></li>
<li><a href="/wiki/Machine_learning_control">Machine learning control</a></li>
<li><a href="/wiki/Machine_perception">Machine perception</a></li>
<li><a href="/wiki/Machine_translation">Machine translation</a></li>
<li><a href="/wiki/Marketing">Marketing</a></li>
<li><a href="/wiki/Automated_medical_diagnosis">Medical diagnosis</a></li>
<li><a href="/wiki/Natural_language_processing">Natural language processing</a></li>
<li><a href="/wiki/Natural-language_understanding">Natural language understanding</a></li>
<li><a href="/wiki/Online_advertising">Online advertising</a></li>
<li><a href="/wiki/Mathematical_optimization">Optimization</a></li>
<li><a href="/wiki/Recommender_system">Recommender systems</a></li>
<li><a href="/wiki/Robot_locomotion">Robot locomotion</a></li>
<li><a href="/wiki/Search_engines">Search engines</a></li>
<li><a href="/wiki/Sentiment_analysis">Sentiment analysis</a></li>
<li><a href="/wiki/Sequence_mining">Sequence mining</a></li>
<li><a href="/wiki/Software_engineering">Software engineering</a></li>
<li><a href="/wiki/Speech_recognition">Speech recognition</a></li>
<li><a href="/wiki/Structural_health_monitoring">Structural health monitoring</a></li>
<li><a href="/wiki/Syntactic_pattern_recognition">Syntactic pattern recognition</a></li>
<li><a href="/wiki/Telecommunication">Telecommunication</a></li>
<li><a href="/wiki/Automated_theorem_proving">Theorem proving</a></li>
<li><a href="/wiki/Time_series">Time-series forecasting</a></li>
<li><a href="/wiki/User_behavior_analytics">User behavior analytics</a></li></ul>
</div>
<p>In 2006, the media-services provider <a href="/wiki/Netflix">Netflix</a> held the first "<a href="/wiki/Netflix_Prize">Netflix Prize</a>" competition to find a program to better predict user preferences and improve the accuracy of its existing Cinematch movie recommendation algorithm by at least 10%. A joint team made up of researchers from <a href="/wiki/AT%26T_Labs">AT&amp;T Labs</a>-Research in collaboration with the teams Big Chaos and Pragmatic Theory built an <a href="/wiki/Ensemble_Averaging">ensemble model</a> to win the Grand Prize in 2009 for $1 million.<sup><a href="#cite_note-81">[81]</a></sup> Shortly after the prize was awarded, Netflix realized that viewers' ratings were not the best indicators of their viewing patterns ("everything is a recommendation") and they changed their recommendation engine accordingly.<sup><a href="#cite_note-82">[82]</a></sup> In 2010 The Wall Street Journal wrote about the firm Rebellion Research and their use of machine learning to predict the financial crisis.<sup><a href="#cite_note-83">[83]</a></sup> In 2012, co-founder of <a href="/wiki/Sun_Microsystems">Sun Microsystems</a>, <a href="/wiki/Vinod_Khosla">Vinod Khosla</a>, predicted that 80% of medical doctors jobs would be lost in the next two decades to automated machine learning medical diagnostic software.<sup><a href="#cite_note-84">[84]</a></sup> In 2014, it was reported that a machine learning algorithm had been applied in the field of art history to study fine art paintings and that it may have revealed previously unrecognized influences among artists.<sup><a href="#cite_note-85">[85]</a></sup> In 2019 <a href="/wiki/Springer_Nature">Springer Nature</a> published the first research book created using machine learning.<sup><a href="#cite_note-86">[86]</a></sup> In 2020, machine learning technology was used to help make diagnoses and aid researchers in developing a cure for COVID-19.<sup><a href="#cite_note-87">[87]</a></sup> Machine learning was recently applied to predict the pro-environmental behavior of travelers.<sup><a href="#cite_note-88">[88]</a></sup> Recently, machine learning technology was also applied to optimize smartphone's performance and thermal behavior based on the user's interaction with the phone.<sup><a href="#cite_note-89">[89]</a></sup><sup><a href="#cite_note-90">[90]</a></sup><sup><a href="#cite_note-91">[91]</a></sup>
</p>
<h2>Limitations[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=34">edit</a>]</h2>
<p>Although machine learning has been transformative in some fields, machine-learning programs often fail to deliver expected results.<sup><a href="#cite_note-92">[92]</a></sup><sup><a href="#cite_note-93">[93]</a></sup><sup><a href="#cite_note-94">[94]</a></sup> Reasons for this are numerous: lack of (suitable) data, lack of access to the data, data bias, privacy problems, badly chosen tasks and algorithms, wrong tools and people, lack of resources, and evaluation problems.<sup><a href="#cite_note-95">[95]</a></sup>
</p><p>In 2018, a self-driving car from <a href="/wiki/Uber">Uber</a> failed to detect a pedestrian, who was killed after a collision.<sup><a href="#cite_note-96">[96]</a></sup> Attempts to use machine learning in healthcare with the <a href="/wiki/Watson_(computer)">IBM Watson</a> system failed to deliver even after years of time and billions of dollars invested.<sup><a href="#cite_note-97">[97]</a></sup><sup><a href="#cite_note-98">[98]</a></sup>
</p><p>Machine learning has been used as a strategy to update the evidence related to a systematic review and increased reviewer burden related to the growth of biomedical literature. While it has improved with training sets, it has not yet developed sufficiently to reduce the workload burden without limiting the necessary sensitivity for the findings research themselves.<sup><a href="#cite_note-99">[99]</a></sup>
</p>
<h3>Bias[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=35">edit</a>]</h3>
<p>Machine learning approaches in particular can suffer from different data biases. A machine learning system trained specifically on current customers may not be able to predict the needs of new customer groups that are not represented in the training data. When trained on man-made data, machine learning is likely to pick up the constitutional and unconscious biases already present in society.<sup><a href="#cite_note-:1-100">[100]</a></sup> Language models learned from data have been shown to contain human-like biases.<sup><a href="#cite_note-101">[101]</a></sup><sup><a href="#cite_note-102">[102]</a></sup> Machine learning systems used for criminal risk assessment have been found to be biased against black people.<sup><a href="#cite_note-103">[103]</a></sup><sup><a href="#cite_note-104">[104]</a></sup> In 2015, Google photos would often tag black people as gorillas,<sup><a href="#cite_note-:2-105">[105]</a></sup> and in 2018 this still was not well resolved, but Google reportedly was still using the workaround to remove all gorillas from the training data, and thus was not able to recognize real gorillas at all.<sup><a href="#cite_note-106">[106]</a></sup> Similar issues with recognizing non-white people have been found in many other systems.<sup><a href="#cite_note-107">[107]</a></sup> In 2016, Microsoft tested a <a href="/wiki/Chatbot">chatbot</a> that learned from Twitter, and it quickly picked up racist and sexist language.<sup><a href="#cite_note-108">[108]</a></sup> Because of such challenges, the effective use of machine learning may take longer to be adopted in other domains.<sup><a href="#cite_note-109">[109]</a></sup> Concern for <a href="/wiki/Fairness_(machine_learning)">fairness</a> in machine learning, that is, reducing bias in machine learning and propelling its use for human good is increasingly expressed by artificial intelligence scientists, including <a href="/wiki/Fei-Fei_Li">Fei-Fei Li</a>, who reminds engineers that "There's nothing artificial about AI...It's inspired by people, it's created by people, and—most importantly—it impacts people. It is a powerful tool we are only just beginning to understand, and that is a profound responsibility."<sup><a href="#cite_note-110">[110]</a></sup>
</p>
<h3>Explainability[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=36">edit</a>]</h3>
<p>Explainable AI (XAI), or Interpretable AI, or Explainable Machine Learning (XML), is artificial intelligence (AI) in which humans can understand the decisions or predictions made by the AI. It contrasts with the "black box" concept in machine learning where even its designers cannot explain why an AI arrived at a specific decision. By refining the mental models of users of AI-powered systems and dismantling their misconceptions, XAI promises to help users perform more effectively. XAI may be an implementation of the social right to explanation.
</p>
<h3>Overfitting[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=37">edit</a>]</h3>
<div><p><a href="/wiki/File:Overfitted_Data.png"></a></p><div><p>The blue line could be an example of overfitting a linear function due to random noise.</p></div></div>
<p>Settling on a bad, overly complex theory gerrymandered to fit all the past training data is known as overfitting. Many systems attempt to reduce overfitting by rewarding a theory in accordance with how well it fits the data but penalizing the theory in accordance with how complex the theory is.<sup><a href="#cite_note-FOOTNOTEDomingos2015Chapter_6,_Chapter_7-10">[10]</a></sup>
</p>
<h3>Other limitations and vulnerabilities[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=38">edit</a>]</h3>
<p>Learners can also disappoint by "learning the wrong lesson". A toy example is that an image classifier trained only on pictures of brown horses and black cats might conclude that all brown patches are likely to be horses.<sup><a href="#cite_note-FOOTNOTEDomingos2015286-111">[111]</a></sup> A real-world example is that, unlike humans, current image classifiers often don't primarily make judgments from the spatial relationship between components of the picture, and they learn relationships between pixels that humans are oblivious to, but that still correlate with images of certain types of real objects. Modifying these patterns on a legitimate image can result in "adversarial" images that the system misclassifies.<sup><a href="#cite_note-112">[112]</a></sup><sup><a href="#cite_note-113">[113]</a></sup>
</p><p>Adversarial vulnerabilities can also result in nonlinear systems, or from non-pattern perturbations. Some systems are so brittle that changing a single adversarial pixel predictably induces misclassification.<sup>[<i><a href="/wiki/Wikipedia:Citation_needed">citation needed</a></i>]</sup> Machine learning models are often vulnerable to manipulation and/or evasion via <a href="/wiki/Adversarial_machine_learning">adversarial machine learning</a>.<sup><a href="#cite_note-114">[114]</a></sup>
</p><p>Researchers have demonstrated how <a href="/wiki/Backdoor_(computing)">backdoors</a> can be placed undetectably into classifying (e.g., for categories "spam" and well-visible "not spam" of posts) machine learning models which are often developed and/or trained by third parties. Parties can change the classification of any input, including in cases for which a type of <a href="/wiki/Algorithmic_transparency">data/software transparency</a> is provided, possibly including <a href="/wiki/White-box_testing">white-box access</a>.<sup><a href="#cite_note-115">[115]</a></sup><sup><a href="#cite_note-116">[116]</a></sup><sup><a href="#cite_note-117">[117]</a></sup>
</p>
<h2>Model assessments[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=39">edit</a>]</h2>
<p>Classification of machine learning models can be validated by accuracy estimation techniques like the <a href="/wiki/Test_set">holdout</a> method, which splits the data in a training and test set (conventionally 2/3 training set and 1/3 test set designation) and evaluates the performance of the training model on the test set. In comparison, the K-fold-<a href="/wiki/Cross-validation_(statistics)">cross-validation</a> method randomly partitions the data into K subsets and then K experiments are performed each respectively considering 1 subset for evaluation and the remaining K-1 subsets for training the model. In addition to the holdout and cross-validation methods, <a href="/wiki/Bootstrapping">bootstrap</a>, which samples n instances with replacement from the dataset, can be used to assess model accuracy.<sup><a href="#cite_note-118">[118]</a></sup>
</p><p>In addition to overall accuracy, investigators frequently report <a href="/wiki/Sensitivity_and_specificity">sensitivity and specificity</a> meaning True Positive Rate (TPR) and True Negative Rate (TNR) respectively. Similarly, investigators sometimes report the <a href="/wiki/False_positive_rate">false positive rate</a> (FPR) as well as the <a href="/wiki/False_negative_rate">false negative rate</a> (FNR). However, these rates are ratios that fail to reveal their numerators and denominators. The <a href="/wiki/Total_operating_characteristic">total operating characteristic</a> (TOC) is an effective method to express a model's diagnostic ability. TOC shows the numerators and denominators of the previously mentioned rates, thus TOC provides more information than the commonly used <a href="/wiki/Receiver_operating_characteristic">receiver operating characteristic</a> (ROC) and ROC's associated area under the curve (AUC).<sup><a href="#cite_note-119">[119]</a></sup>
</p>
<h2>Ethics[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=40">edit</a>]</h2>
<p>Machine learning poses a host of <a href="/wiki/Machine_ethics">ethical questions</a>. Systems that are trained on datasets collected with biases may exhibit these biases upon use (<a href="/wiki/Algorithmic_bias">algorithmic bias</a>), thus digitizing cultural prejudices.<sup><a href="#cite_note-120">[120]</a></sup> For example, in 1988, the UK's Commission for Racial Equality found that St. George's Medical School had been using a computer program trained from data of previous admissions staff and this program had denied nearly 60 candidates who were found to be either women or had non-European sounding names.<sup><a href="#cite_note-:1-100">[100]</a></sup> Using job hiring data from a firm with racist hiring policies may lead to a machine learning system duplicating the bias by scoring job applicants by similarity to previous successful applicants.<sup><a href="#cite_note-Edionwe_Outline-121">[121]</a></sup><sup><a href="#cite_note-Jeffries_Outline-122">[122]</a></sup> Responsible <a href="/wiki/Data_collection">collection of data</a> and documentation of algorithmic rules used by a system thus is a critical part of machine learning.
</p><p>AI can be well-equipped to make decisions in technical fields, which rely heavily on data and historical information. These decisions rely on the objectivity and logical reasoning.<sup><a href="#cite_note-123">[123]</a></sup> Because human languages contain biases, machines trained on language <i><a href="/wiki/Text_corpus">corpora</a></i> will necessarily also learn these biases.<sup><a href="#cite_note-124">[124]</a></sup><sup><a href="#cite_note-125">[125]</a></sup>
</p><p>Other forms of ethical challenges, not related to personal biases, are seen in health care. There are concerns among health care professionals that these systems might not be designed in the public's interest but as income-generating machines.<sup><a href="#cite_note-126">[126]</a></sup> This is especially true in the United States where there is a long-standing ethical dilemma of improving health care, but also increase profits. For example, the algorithms could be designed to provide patients with unnecessary tests or medication in which the algorithm's proprietary owners hold stakes. There is potential for machine learning in health care to provide professionals an additional tool to diagnose, medicate, and plan recovery paths for patients, but this requires these biases to be mitigated.<sup><a href="#cite_note-127">[127]</a></sup>
</p>
<h2>Hardware[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=41">edit</a>]</h2>
<p>Since the 2010s, advances in both machine learning algorithms and computer hardware have led to more efficient methods for training <a href="/wiki/Deep_neural_network">deep neural networks</a> (a particular narrow subdomain of machine learning) that contain many layers of non-linear hidden units.<sup><a href="#cite_note-128">[128]</a></sup> By 2019, graphic processing units (<a href="/wiki/GPU">GPUs</a>), often with AI-specific enhancements, had displaced CPUs as the dominant method of training large-scale commercial cloud AI.<sup><a href="#cite_note-129">[129]</a></sup> <a href="/wiki/OpenAI">OpenAI</a> estimated the hardware computing used in the largest deep learning projects from AlexNet (2012) to AlphaZero (2017), and found a 300,000-fold increase in the amount of compute required, with a doubling-time trendline of 3.4 months.<sup><a href="#cite_note-130">[130]</a></sup><sup><a href="#cite_note-131">[131]</a></sup>
</p>
<h3>Neuromorphic/Physical Neural Networks[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=42">edit</a>]</h3>
<p>A <a href="/wiki/Physical_neural_network">physical neural network</a> or <a href="/wiki/Neuromorphic_engineering">Neuromorphic computer</a> is a type of <a href="/wiki/Artificial_neural_network">artificial neural network</a> in which an electrically adjustable material is used to emulate the function of a <a href="/wiki/Chemical_synapse">neural synapse</a>. "Physical" neural network is used to emphasize the reliance on physical hardware used to emulate <a href="/wiki/Neurons">neurons</a> as opposed to software-based approaches. More generally the term is applicable to other artificial neural networks in which a <a href="/wiki/Memristor">memristor</a> or other electrically adjustable resistance material is used to emulate a neural synapse.<sup><a href="#cite_note-132">[132]</a></sup><sup><a href="#cite_note-133">[133]</a></sup>
</p>
<h3>Embedded Machine Learning[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=43">edit</a>]</h3>
<p><b>Embedded Machine Learning</b> is a sub-field of machine learning, where the machine learning model is run on <a href="/wiki/Embedded_systems">embedded systems</a> with limited computing resources such as <a href="/wiki/Wearable_computer">wearable computers</a>, <a href="/wiki/Edge_device">edge devices</a> and <a href="/wiki/Microcontrollers">microcontrollers</a>.<sup><a href="#cite_note-134">[134]</a></sup><sup><a href="#cite_note-135">[135]</a></sup><sup><a href="#cite_note-136">[136]</a></sup> Running machine learning model in embedded devices removes the need for transferring and storing data on cloud servers for further processing, henceforth, reducing data breaches and privacy leaks happening because of transferring data, and also minimizes theft of intellectual properties, personal data and business secrets. Embedded Machine Learning could be applied through several techniques including <a href="/wiki/Hardware_acceleration">hardware acceleration</a>,<sup><a href="#cite_note-137">[137]</a></sup><sup><a href="#cite_note-138">[138]</a></sup> using <a href="/wiki/Approximate_computing">approximate computing</a>,<sup><a href="#cite_note-139">[139]</a></sup> optimization of machine learning models and many more.<sup><a href="#cite_note-140">[140]</a></sup><sup><a href="#cite_note-141">[141]</a></sup>
</p>
<h2>Software[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=44">edit</a>]</h2>
<p><a href="/wiki/Software_suite">Software suites</a> containing a variety of machine learning algorithms include the following:
</p>
<h3>Free and open-source software[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=45">edit</a>]</h3>
<div>
<ul><li><a href="/wiki/Caffe_(software)">Caffe</a></li>
<li><a href="/wiki/Deeplearning4j">Deeplearning4j</a></li>
<li><a href="/wiki/DeepSpeed">DeepSpeed</a></li>
<li><a href="/wiki/ELKI">ELKI</a></li>
<li><a href="/wiki/Google_JAX">Google JAX</a></li>
<li><a href="/wiki/Infer.NET">Infer.NET</a></li>
<li><a href="/wiki/Keras">Keras</a></li>
<li><a href="/wiki/Kubeflow">Kubeflow</a></li>
<li><a href="/wiki/LightGBM">LightGBM</a></li>
<li><a href="/wiki/Apache_Mahout">Mahout</a></li>
<li><a href="/wiki/Mallet_(software_project)">Mallet</a></li>
<li><a href="/wiki/Microsoft_Cognitive_Toolkit">Microsoft Cognitive Toolkit</a></li>
<li><a href="/wiki/ML.NET">ML.NET</a></li>
<li><a href="/wiki/Mlpack">mlpack</a></li>
<li>MLFlow</li>
<li><a href="/wiki/MXNet">MXNet</a></li>
<li><a href="/wiki/Neural_Lab">Neural Lab</a></li>
<li><a href="/wiki/OpenNN">OpenNN</a></li>
<li><a href="/wiki/Orange_(software)">Orange</a></li>
<li><a href="/wiki/Pandas_(software)">pandas (software)</a></li>
<li><a href="/wiki/ROOT">ROOT</a> (TMVA with ROOT)</li>
<li><a href="/wiki/Scikit-learn">scikit-learn</a></li>
<li><a href="/wiki/Shogun_(toolbox)">Shogun</a></li>
<li><a href="/wiki/Apache_Spark#MLlib_Machine_Learning_Library">Spark MLlib</a></li>
<li><a href="/wiki/Apache_SystemML">SystemML</a></li>
<li><a href="/wiki/TensorFlow">TensorFlow</a></li>
<li><a href="/wiki/Torch_(machine_learning)">Torch</a> / <a href="/wiki/PyTorch">PyTorch</a></li>
<li><a href="/wiki/Weka_(machine_learning)">Weka</a> / <a href="/wiki/MOA_(Massive_Online_Analysis)">MOA</a></li>
<li><a href="/wiki/XGBoost">XGBoost</a></li>
<li><a href="/wiki/Yooreeka">Yooreeka</a></li></ul>
</div>
<h3>Proprietary software with free and open-source editions[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=46">edit</a>]</h3>
<ul><li><a href="/wiki/KNIME">KNIME</a></li>
<li><a href="/wiki/RapidMiner">RapidMiner</a></li></ul>
<h3>Proprietary software[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=47">edit</a>]</h3>
<div>
<ul><li><a href="/wiki/Amazon_Machine_Learning">Amazon Machine Learning</a></li>
<li><a href="/wiki/Angoss">Angoss</a> KnowledgeSTUDIO</li>
<li><a href="/wiki/Azure_Machine_Learning">Azure Machine Learning</a></li>
<li>Ayasdi</li>
<li><a href="/wiki/IBM_Watson_Studio">IBM Watson Studio</a></li>
<li><a href="/wiki/Google_Cloud_Platform#Cloud_AI">Google Cloud Vertex AI</a></li>
<li><a href="/wiki/Google_APIs">Google Prediction API</a></li>
<li><a href="/wiki/SPSS_Modeler">IBM SPSS Modeler</a></li>
<li><a href="/wiki/KXEN_Inc.">KXEN Modeler</a></li>
<li><a href="/wiki/LIONsolver">LIONsolver</a></li>
<li><a href="/wiki/Mathematica">Mathematica</a></li>
<li><a href="/wiki/MATLAB">MATLAB</a></li>
<li><a href="/wiki/Neural_Designer">Neural Designer</a></li>
<li><a href="/wiki/NeuroSolutions">NeuroSolutions</a></li>
<li><a href="/wiki/Oracle_Data_Mining">Oracle Data Mining</a></li>
<li><a href="/wiki/Oracle_Cloud#Platform_as_a_Service_(PaaS)">Oracle AI Platform Cloud Service</a></li>
<li><a href="/wiki/PolyAnalyst">PolyAnalyst</a></li>
<li><a href="/wiki/RCASE">RCASE</a></li>
<li><a href="/wiki/SAS_(software)#Components">SAS Enterprise Miner</a></li>
<li><a href="/wiki/SequenceL">SequenceL</a></li>
<li><a href="/wiki/Splunk">Splunk</a></li>
<li><a href="/wiki/STATISTICA">STATISTICA</a> Data Miner</li></ul>
</div>
<h2>Journals[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=48">edit</a>]</h2>
<ul><li><a href="/wiki/Journal_of_Machine_Learning_Research">Journal of Machine Learning Research</a></li>
<li><a href="/wiki/Machine_Learning_(journal)">Machine Learning</a></li>
<li><a href="/wiki/Nature_Machine_Intelligence">Nature Machine Intelligence</a></li>
<li><a href="/wiki/Neural_Computation_(journal)">Neural Computation</a></li>
<li>IEEE Transactions on Pattern Analysis and Machine Intelligence</li></ul>
<h2>Conferences[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=49">edit</a>]</h2>
<ul><li><a href="/wiki/AAAI_Conference_on_Artificial_Intelligence">AAAI Conference on Artificial Intelligence</a></li>
<li><a href="/wiki/Association_for_Computational_Linguistics">Association for Computational Linguistics (<b>ACL</b>)</a></li>
<li><a href="/wiki/European_Conference_on_Machine_Learning_and_Principles_and_Practice_of_Knowledge_Discovery_in_Databases">European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (<b>ECML PKDD</b>)</a></li>
<li><a href="/wiki/International_Conference_on_Computational_Intelligence_Methods_for_Bioinformatics_and_Biostatistics">International Conference on Computational Intelligence Methods for Bioinformatics and Biostatistics (<b>CIBB</b>)</a></li>
<li><a href="/wiki/International_Conference_on_Machine_Learning">International Conference on Machine Learning (<b>ICML</b>)</a></li>
<li><a href="/wiki/International_Conference_on_Learning_Representations">International Conference on Learning Representations (<b>ICLR</b>)</a></li>
<li><a href="/wiki/International_Conference_on_Intelligent_Robots_and_Systems">International Conference on Intelligent Robots and Systems (<b>IROS</b>)</a></li>
<li><a href="/wiki/Conference_on_Knowledge_Discovery_and_Data_Mining">Conference on Knowledge Discovery and Data Mining (<b>KDD</b>)</a></li>
<li><a href="/wiki/Conference_on_Neural_Information_Processing_Systems">Conference on Neural Information Processing Systems (<b>NeurIPS</b>)</a></li></ul>
<h2>See also[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=50">edit</a>]</h2>
<ul><li><a href="/wiki/Automated_machine_learning">Automated machine learning</a> – Process of automating the application of machine learning</li>
<li><a href="/wiki/Big_data">Big data</a> – Information assets characterized by high volume, velocity, and variety</li>
<li><a href="/wiki/Differentiable_programming">Differentiable programming</a> – Programming paradigm</li>
<li><a href="/wiki/List_of_important_publications_in_computer_science#Machine_learning">List of important publications in machine learning</a></li>
<li><a href="/wiki/List_of_datasets_for_machine-learning_research">List of datasets for machine-learning research</a></li></ul>
<h2>References[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=51">edit</a>]</h2>
<div>
<ol>
<li><b><a href="#cite_ref-1">^</a></b> <cite><a href="/wiki/Tom_M._Mitchell">Mitchell, Tom</a> (1997). <a href="http://www.cs.cmu.edu/~tom/mlbook.html"><i>Machine Learning</i></a>. New York: McGraw Hill. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-042807-7"><bdi>0-07-042807-7</bdi></a>. <a href="/wiki/OCLC_(identifier)">OCLC</a> <a href="//www.worldcat.org/oclc/36417892">36417892</a>. <a href="https://web.archive.org/web/20200407075538/http://www.cs.cmu.edu/~tom/mlbook.html">Archived</a> from the original on 2020-04-07. Retrieved 2020-04-09.</cite>
</li>
<li><b><a href="#cite_ref-2">^</a></b> The definition "without being explicitly programmed" is often attributed to <a href="/wiki/Arthur_Samuel_(computer_scientist)">Arthur Samuel</a>, who coined the term "machine learning" in 1959, but the phrase is not found verbatim in this publication, and may be a <a href="/wiki/Paraphrase">paraphrase</a> that appeared later. Confer "Paraphrasing Arthur Samuel (1959), the question is: How can computers learn to solve problems without being explicitly programmed?" in <cite>Koza, John R.; Bennett, Forrest H.; Andre, David; Keane, Martin A. (1996). "Automated Design of Both the Topology and Sizing of Analog Electrical Circuits Using Genetic Programming". <i>Artificial Intelligence in Design '96</i>. Artificial Intelligence in Design '96. Springer, Dordrecht. pp. 151–170. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2F978-94-009-0279-4_9">10.1007/978-94-009-0279-4_9</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-94-010-6610-5"><bdi>978-94-010-6610-5</bdi></a>.</cite>
</li>
<li><b><a href="#cite_ref-tvt_3-0">^</a></b> Hu, J.; Niu, H.; Carrasco, J.; Lennox, B.; Arvin, F., "<a href="https://ieeexplore.ieee.org/document/9244647">Voronoi-Based Multi-Robot Autonomous Exploration in Unknown Environments via Deep Reinforcement Learning</a> <a href="https://web.archive.org/web/20201116193020/https://ieeexplore.ieee.org/document/9244647">Archived</a> 2020-11-16 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a>" IEEE Transactions on Vehicular Technology, 2020.
</li>
<li><b><a href="#cite_ref-4">^</a></b> <cite>Yoosefzadeh-Najafabadi, Mohsen; Hugh, Earl; Tulpan, Dan; Sulik, John; Eskandari, Milad (2021). <a href="//www.ncbi.nlm.nih.gov/pmc/articles/PMC7835636">"Application of Machine Learning Algorithms in Plant Breeding: Predicting Yield From Hyperspectral Reflectance in Soybean?"</a>. <i>Front. Plant Sci</i>. <b>11</b>: 624273. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.3389%2Ffpls.2020.624273">10.3389/fpls.2020.624273</a>. <a href="/wiki/PMC_(identifier)">PMC</a> <a href="//www.ncbi.nlm.nih.gov/pmc/articles/PMC7835636">7835636</a>. <a href="/wiki/PMID_(identifier)">PMID</a> <a href="//pubmed.ncbi.nlm.nih.gov/33510761">33510761</a>.</cite>
</li>
<li>^ <a href="#cite_ref-bishop2006_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-bishop2006_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-bishop2006_5-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-bishop2006_5-3"><sup><i><b>d</b></i></sup></a> <cite><a href="/wiki/Christopher_M._Bishop">Bishop, C. M.</a> (2006), <i>Pattern Recognition and Machine Learning</i>, Springer, <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-31073-2"><bdi>978-0-387-31073-2</bdi></a></cite>
</li>
<li><b><a href="#cite_ref-6">^</a></b> Machine learning and pattern recognition "can be viewed as two facets of the same field."<sup><a href="#cite_note-bishop2006-5">[5]</a></sup><sup>: vii </sup>
</li>
<li><b><a href="#cite_ref-7">^</a></b> <cite><a href="/wiki/Jerome_H._Friedman">Friedman, Jerome H.</a> (1998). "Data Mining and Statistics: What's the connection?". <i>Computing Science and Statistics</i>. <b>29</b> (1): 3–9.</cite>
</li>
<li><b><a href="#cite_ref-8">^</a></b> <cite><a href="https://www.ibm.com/cloud/learn/machine-learning">"What is Machine Learning?"</a>. <i>www.ibm.com</i>. <a href="https://web.archive.org/web/20210813154117/https://www.ibm.com/cloud/learn/machine-learning">Archived</a> from the original on 2021-08-13. Retrieved 2021-08-15.</cite>
</li>
<li><b><a href="#cite_ref-9">^</a></b> <cite>Zhou, Victor (2019-12-20). <a href="https://towardsdatascience.com/machine-learning-for-beginners-an-introduction-to-neural-networks-d49f22d238f9">"Machine Learning for Beginners: An Introduction to Neural Networks"</a>. <i>Medium</i>. <a href="https://web.archive.org/web/20220309053518/https://towardsdatascience.com/machine-learning-for-beginners-an-introduction-to-neural-networks-d49f22d238f9">Archived</a> from the original on 2022-03-09. Retrieved 2021-08-15.</cite>
</li>
<li>^ <a href="#cite_ref-FOOTNOTEDomingos2015Chapter_6,_Chapter_7_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEDomingos2015Chapter_6,_Chapter_7_10-1"><sup><i><b>b</b></i></sup></a> <a href="#CITEREFDomingos2015">Domingos 2015</a>, Chapter 6, Chapter 7.
</li>
<li>^ <a href="#cite_ref-Alpaydin2020_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Alpaydin2020_11-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Alpaydin2020_11-2"><sup><i><b>c</b></i></sup></a> <cite>Ethem Alpaydin (2020). <i>Introduction to Machine Learning</i> (Fourth ed.). <a href="/wiki/MIT">MIT</a>. pp. xix, 1–3, 13–18. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0262043793"><bdi>978-0262043793</bdi></a>.</cite>
</li>
<li><b><a href="#cite_ref-Samuel_12-0">^</a></b> <cite>Samuel, Arthur (1959). "Some Studies in Machine Learning Using the Game of Checkers". <i>IBM Journal of Research and Development</i>. <b>3</b> (3): 210–229. <a href="/wiki/CiteSeerX_(identifier)">CiteSeerX</a> <a href="//citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.368.2254">10.1.1.368.2254</a>. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1147%2Frd.33.0210">10.1147/rd.33.0210</a>.</cite>
</li>
<li><b><a href="#cite_ref-13">^</a></b> R. Kohavi and F. Provost, "Glossary of terms," Machine Learning, vol. 30, no. 2–3, pp. 271–274, 1998.
</li>
<li><b><a href="#cite_ref-cyberthreat_14-0">^</a></b> <cite>Gerovitch, Slava (9 April 2015). <a href="https://web.archive.org/web/20210922175839/https://nautil.us/issue/23/Dominoes/how-the-computer-got-its-revenge-on-the-soviet-union">"How the Computer Got Its Revenge on the Soviet Union"</a>. <i>Nautilus</i>. Archived from <a href="https://nautil.us/issue/23/dominoes/how-the-computer-got-its-revenge-on-the-soviet-union">the original</a> on 22 September 2021. Retrieved 19 September 2021.</cite>
</li>
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<li><b><a href="#cite_ref-135">^</a></b> <cite><a href="https://analyticsindiamag.com/a-beginners-guide-to-machine-learning-for-embedded-systems/">"A Beginner's Guide To Machine learning For Embedded Systems"</a>. <i>Analytics India Magazine</i>. 2021-06-02. <a href="https://web.archive.org/web/20220118182754/https://analyticsindiamag.com/a-beginners-guide-to-machine-learning-for-embedded-systems/">Archived</a> from the original on 2022-01-18. Retrieved 2022-01-17.</cite>
</li>
<li><b><a href="#cite_ref-136">^</a></b> <cite>Synced (2022-01-12). <a href="https://syncedreview.com/2022/01/12/deepmind-podracer-tpu-based-rl-frameworks-deliver-exceptional-performance-at-low-cost-183/">"Google, Purdue &amp; Harvard U's Open-Source Framework for TinyML Achieves up to 75x Speedups on FPGAs | Synced"</a>. <i>syncedreview.com</i>. <a href="https://web.archive.org/web/20220118182404/https://syncedreview.com/2022/01/12/deepmind-podracer-tpu-based-rl-frameworks-deliver-exceptional-performance-at-low-cost-183/">Archived</a> from the original on 2022-01-18. Retrieved 2022-01-17.</cite>
</li>
<li><b><a href="#cite_ref-137">^</a></b> <cite>Giri, Davide; Chiu, Kuan-Lin; Di Guglielmo, Giuseppe; Mantovani, Paolo; Carloni, Luca P. (2020-06-15). <a href="https://ieeexplore.ieee.org/abstract/document/9116317?casa_token=5I_Tmgrrbu4AAAAA:v7pDHPEWlRuo2Vk3pU06194PO0-W21UOdyZqADrZxrRdPBZDMLwQrjJSAHUhHtzJmLu_VdgW">"ESP4ML: Platform-Based Design of Systems-on-Chip for Embedded Machine Learning"</a>. <i>2020 Design, Automation Test in Europe Conference Exhibition (DATE)</i>: 1049–1054. <a href="/wiki/ArXiv_(identifier)">arXiv</a>:<a href="//arxiv.org/abs/2004.03640">2004.03640</a>. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.23919%2FDATE48585.2020.9116317">10.23919/DATE48585.2020.9116317</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-9819263-4-7"><bdi>978-3-9819263-4-7</bdi></a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:210928161">210928161</a>. <a href="https://web.archive.org/web/20220118182342/https://ieeexplore.ieee.org/abstract/document/9116317?casa_token=5I_Tmgrrbu4AAAAA:v7pDHPEWlRuo2Vk3pU06194PO0-W21UOdyZqADrZxrRdPBZDMLwQrjJSAHUhHtzJmLu_VdgW">Archived</a> from the original on 2022-01-18. Retrieved 2022-01-17.</cite>
</li>
<li><b><a href="#cite_ref-138">^</a></b> <cite>Louis, Marcia Sahaya; Azad, Zahra; Delshadtehrani, Leila; Gupta, Suyog; Warden, Pete; Reddi, Vijay Janapa; Joshi, Ajay (2019). <a href="https://edge.seas.harvard.edu/publications/towards-deep-learning-using-tensorflow-lite-risc-v">"Towards Deep Learning using TensorFlow Lite on RISC-V"</a>. <i><a href="/wiki/Harvard_University">Harvard University</a></i>. <a href="https://web.archive.org/web/20220117031909/https://edge.seas.harvard.edu/publications/towards-deep-learning-using-tensorflow-lite-risc-v">Archived</a> from the original on 2022-01-17. Retrieved 2022-01-17.</cite>
</li>
<li><b><a href="#cite_ref-139">^</a></b> <cite>Ibrahim, Ali; Osta, Mario; Alameh, Mohamad; Saleh, Moustafa; Chible, Hussein; Valle, Maurizio (2019-01-21). <a href="https://ieeexplore.ieee.org/abstract/document/8617877?casa_token=arUW5Oy-tzwAAAAA:I9x6edlfskM6kGNFUN9zAFrjEBv_8kYTz7ERTxtXu9jAqdrYCcDbbwjBdgwXvb6QAH_-0VJJ">"Approximate Computing Methods for Embedded Machine Learning"</a>. <i>2018 25th IEEE International Conference on Electronics, Circuits and Systems (ICECS)</i>: 845–848. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1109%2FICECS.2018.8617877">10.1109/ICECS.2018.8617877</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-5386-9562-3"><bdi>978-1-5386-9562-3</bdi></a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:58670712">58670712</a>. <a href="https://web.archive.org/web/20220117031855/https://ieeexplore.ieee.org/abstract/document/8617877?casa_token=arUW5Oy-tzwAAAAA:I9x6edlfskM6kGNFUN9zAFrjEBv_8kYTz7ERTxtXu9jAqdrYCcDbbwjBdgwXvb6QAH_-0VJJ">Archived</a> from the original on 2022-01-17. Retrieved 2022-01-17.</cite>
</li>
<li><b><a href="#cite_ref-140">^</a></b> <cite><a href="https://dblp.org/rec/journals/corr/abs-1903-01855.html">"dblp: TensorFlow Eager: A Multi-Stage, Python-Embedded DSL for Machine Learning"</a>. <i>dblp.org</i>. <a href="https://web.archive.org/web/20220118182335/https://dblp.org/rec/journals/corr/abs-1903-01855.html">Archived</a> from the original on 2022-01-18. Retrieved 2022-01-17.</cite>
</li>
<li><b><a href="#cite_ref-141">^</a></b> <cite>Branco, Sérgio; Ferreira, André G.; Cabral, Jorge (2019-11-05). <a href="https://doi.org/10.3390%2Felectronics8111289">"Machine Learning in Resource-Scarce Embedded Systems, FPGAs, and End-Devices: A Survey"</a>. <i>Electronics</i>. <b>8</b> (11): 1289. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.3390%2Felectronics8111289">10.3390/electronics8111289</a>. <a href="/wiki/ISSN_(identifier)">ISSN</a> <a href="//www.worldcat.org/issn/2079-9292">2079-9292</a>.</cite>
</li>
</ol></div>
<h2>Sources[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=52">edit</a>]</h2>
<ul><li><cite><a href="/wiki/Pedro_Domingos">Domingos, Pedro</a> (September 22, 2015). <i>The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World</i>. <a href="/wiki/Basic_Books">Basic Books</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0465065707"><bdi>978-0465065707</bdi></a>.</cite></li>
<li><cite><a href="/wiki/Nils_Nilsson_(researcher)">Nilsson, Nils</a> (1998). <a href="https://archive.org/details/artificialintell0000nils"><i>Artificial Intelligence: A New Synthesis</i></a>. Morgan Kaufmann. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-55860-467-4"><bdi>978-1-55860-467-4</bdi></a>. <a href="https://web.archive.org/web/20200726131654/https://archive.org/details/artificialintell0000nils">Archived</a> from the original on 26 July 2020. Retrieved 18 November 2019.</cite></li>
<li><cite><a href="/wiki/Stuart_J._Russell">Russell, Stuart J.</a>; <a href="/wiki/Peter_Norvig">Norvig, Peter</a> (2003), <a href="http://aima.cs.berkeley.edu/"><i>Artificial Intelligence: A Modern Approach</i></a> (2nd ed.), Upper Saddle River, New Jersey: Prentice Hall, <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-790395-2"><bdi>0-13-790395-2</bdi></a></cite>.</li>
<li><cite>Poole, David; <a href="/wiki/Alan_Mackworth">Mackworth, Alan</a>; Goebel, Randy (1998). <a href="https://archive.org/details/computationalint00pool"><i>Computational Intelligence: A Logical Approach</i></a>. New York: Oxford University Press. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-510270-3"><bdi>978-0-19-510270-3</bdi></a>. <a href="https://web.archive.org/web/20200726131436/https://archive.org/details/computationalint00pool">Archived</a> from the original on 26 July 2020. Retrieved 22 August 2020.</cite></li></ul>
<h2>Further reading[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=53">edit</a>]</h2>
<div>
<ul><li>Nils J. Nilsson, <i><a href="https://ai.stanford.edu/people/nilsson/mlbook.html">Introduction to Machine Learning</a> <a href="https://web.archive.org/web/20190816182600/http://ai.stanford.edu/people/nilsson/mlbook.html">Archived</a> 2019-08-16 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a></i>.</li>
<li><a href="/wiki/Trevor_Hastie">Trevor Hastie</a>, <a href="/wiki/Robert_Tibshirani">Robert Tibshirani</a> and <a href="/wiki/Jerome_H._Friedman">Jerome H. Friedman</a> (2001). <i><a href="https://web.stanford.edu/~hastie/ElemStatLearn/">The Elements of Statistical Learning</a> <a href="https://web.archive.org/web/20131027220938/http://www-stat.stanford.edu/%7Etibs/ElemStatLearn//">Archived</a> 2013-10-27 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a></i>, Springer. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-387-95284-5">0-387-95284-5</a>.</li>
<li><a href="/wiki/Pedro_Domingos">Pedro Domingos</a> (September 2015), <i><a href="/wiki/The_Master_Algorithm">The Master Algorithm</a></i>, Basic Books, <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-465-06570-7">978-0-465-06570-7</a></li>
<li>Ian H. Witten and Eibe Frank (2011). <i>Data Mining: Practical machine learning tools and techniques</i> Morgan Kaufmann, 664pp., <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-374856-0">978-0-12-374856-0</a>.</li>
<li>Ethem Alpaydin (2004). <i>Introduction to Machine Learning</i>, MIT Press, <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-01243-0">978-0-262-01243-0</a>.</li>
<li><a href="/wiki/David_J._C._MacKay">David J. C. MacKay</a>. <i><a href="http://www.inference.phy.cam.ac.uk/mackay/itila/book.html">Information Theory, Inference, and Learning Algorithms</a> <a href="https://web.archive.org/web/20160217105359/http://www.inference.phy.cam.ac.uk/mackay/itila/book.html">Archived</a> 2016-02-17 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a></i> Cambridge: Cambridge University Press, 2003. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-64298-1">0-521-64298-1</a></li>
<li><a href="/wiki/Richard_O._Duda">Richard O. Duda</a>, <a href="/wiki/Peter_E._Hart">Peter E. Hart</a>, David G. Stork (2001) <i>Pattern classification</i> (2nd edition), Wiley, New York, <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-05669-3">0-471-05669-3</a>.</li>
<li><a href="/wiki/Christopher_Bishop">Christopher Bishop</a> (1995). <i>Neural Networks for Pattern Recognition</i>, Oxford University Press. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-853864-2">0-19-853864-2</a>.</li>
<li>Stuart Russell &amp; Peter Norvig, (2009). <i><a href="http://aima.cs.berkeley.edu/">Artificial Intelligence – A Modern Approach</a> <a href="https://web.archive.org/web/20110228023805/http://aima.cs.berkeley.edu/">Archived</a> 2011-02-28 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a></i>. Pearson, <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9789332543515">9789332543515</a>.</li>
<li><a href="/wiki/Ray_Solomonoff">Ray Solomonoff</a>, <i>An Inductive Inference Machine</i>, IRE Convention Record, Section on Information Theory, Part 2, pp., 56–62, 1957.</li>
<li><a href="/wiki/Ray_Solomonoff">Ray Solomonoff</a>, <i><a href="http://world.std.com/~rjs/indinf56.pdf">An Inductive Inference Machine</a> <a href="https://web.archive.org/web/20110426161749/http://world.std.com/~rjs/indinf56.pdf">Archived</a> 2011-04-26 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a></i> A privately circulated report from the 1956 <a href="/wiki/Dartmouth_workshop">Dartmouth Summer Research Conference on AI</a>.</li>
<li>Kevin P. Murphy (2021). <i><a href="https://probml.github.io/pml-book/book1.html">Probabilistic Machine Learning: An Introduction</a> <a href="https://web.archive.org/web/20210411153246/https://probml.github.io/pml-book/book1.html">Archived</a> 2021-04-11 at the <a href="/wiki/Wayback_Machine">Wayback Machine</a></i>, MIT Press.</li></ul>
</div>
<h2>External links[<a href="/w/index.php?title=Machine_learning&amp;action=edit&amp;section=54">edit</a>]</h2>
<ul><li><a href="/wiki/File:Wikiquote-logo.svg"></a> Quotations related to <a href="https://en.wikiquote.org/wiki/Special:Search/Machine_learning">Machine learning</a> at Wikiquote</li>
<li><a href="https://web.archive.org/web/20171230081341/http://machinelearning.org/">International Machine Learning Society</a></li>
<li><a href="https://mloss.org/">mloss</a> is an academic database of open-source machine learning software.</li></ul>
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 Contents

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 * (Top)
 * 1 Overview
 * 2 History and relationships to other fields
 + 2.1 Artificial intelligence
 + 2.2 Data mining
 + 2.3 Optimization
 + 2.4 Generalization
 + 2.5 Statistics
 + 2.6 Physics
 * 3 Theory
 * 4 Approaches
 + 4.1 Supervised learning
 + 4.2 Unsupervised learning
 + 4.3 Semi-supervised learning
 + 4.4 Reinforcement learning
 + 4.5 Dimensionality reduction
 + 4.6 Other types
 o 4.6.1 Self-learning
 o 4.6.2 Feature learning
 o 4.6.3 Sparse dictionary learning
 o 4.6.4 Anomaly detection
 o 4.6.5 Robot learning
 o 4.6.6 Association rules
 + 4.7 Models
 o 4.7.1 Artificial neural networks
 o 4.7.2 Decision trees
 o 4.7.3 Support-vector machines
 o 4.7.4 Regression analysis
 o 4.7.5 Bayesian networks
 o 4.7.6 Gaussian processes
 o 4.7.7 Genetic algorithms
 + 4.8 Training models
 o 4.8.1 Federated learning
 * 5 Applications
 * 6 Limitations
 + 6.1 Bias
 + 6.2 Explainability
 + 6.3 Overfitting
 + 6.4 Other limitations and vulnerabilities
 * 7 Model assessments
 * 8 Ethics
 * 9 Hardware
 + 9.1 Neuromorphic/Physical Neural Networks
 + 9.2 Embedded Machine Learning
 * 10 Software
 + 10.1 Free and open-source software
 + 10.2 Proprietary software with free and open-source editions
 + 10.3 Proprietary software
 * 11 Journals
 * 12 Conferences
 * 13 See also
 * 14 References
 * 15 Sources
 * 16 Further reading
 * 17 External links
 Toggle the table of contents

 Machine learning

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 From Wikipedia, the free encyclopedia
 For the journal, see Machine Learning (journal).
 "Statistical learning" redirects here. For statistical learning in linguistics, see statistical learning in language acquisition.
 Part of a series on 
 Machine learning 
 and data mining 
  
 Paradigms 
 * Supervised learning 
 * Unsupervised learning 
 * Online learning 
 * Batch learning 
 * Semi-supervised learning 
 * Self-supervised learning 
 * Reinforcement learning 
 Problems 
 * Classification 
 * Regression 
 * Clustering 
 * dimension reduction 
 * density estimation 
 * Anomaly detection 
 * Data Cleaning 
 * AutoML 
 * Association rules 
 * Structured prediction 
 * Feature engineering 
 * Feature learning 
 * Learning to rank 
 * Grammar induction 
 Supervised learning 
 ( classification • regression ) 
 * Decision trees 
 * Ensembles 
 + Bagging 
 + Boosting 
 + Random forest 
 * k-NN 
 * Linear regression 
 * Naive Bayes 
 * Artificial neural networks 
 * Logistic regression 
 * Perceptron 
 * Relevance vector machine (RVM) 
 * Support vector machine (SVM) 
 Clustering 
 * BIRCH 
 * CURE 
 * Hierarchical 
 * k-means 
 * Fuzzy 
 * Expectation–maximization (EM) 
  
 * DBSCAN 
 * OPTICS 
 * Mean shift 
 Dimensionality reduction 
 * Factor analysis 
 * CCA 
 * ICA 
 * LDA 
 * NMF 
 * PCA 
 * PGD 
 * t-SNE 
 * SDL 
 Structured prediction 
 * Graphical models 
 + Bayes net 
 + Conditional random field 
 + Hidden Markov 
 Anomaly detection 
 * RANSAC 
 * k-NN 
 * Local outlier factor 
 * Isolation forest 
 Artificial neural network 
 * Autoencoder 
 * Cognitive computing 
 * Deep learning 
 * DeepDream 
 * Multilayer perceptron 
 * RNN 
 + LSTM 
 + GRU 
 + ESN 
 + reservoir computing 
 * Restricted Boltzmann machine 
 * GAN 
 * SOM 
 * Convolutional neural network 
 + U-Net 
 * Transformer 
 + Vision 
 * Spiking neural network 
 * Memtransistor 
 * Electrochemical RAM (ECRAM) 
 Reinforcement learning 
 * Q-learning 
 * SARSA 
 * Temporal difference (TD) 
 * Multi-agent 
 + Self-play 
 Learning with humans 
 * Active learning 
 * Crowdsourcing 
 * Human-in-the-loop 
 Model diagnostics 
 * Learning curve 
 Theory 
 * Kernel machines 
 * Bias–variance tradeoff 
 * Computational learning theory 
 * Empirical risk minimization 
 * Occam learning 
 * PAC learning 
 * Statistical learning 
 * VC theory 
 Machine-learning venues 
 * NeurIPS 
 * ICML 
 * ICLR 
 * ML 
 * JMLR 
 Related articles 
 * Glossary of artificial intelligence 
 * List of datasets for machine-learning research
 * Outline of machine learning 
 * v 
 * t 
 * e 
 
 Part of a series on 
 Artificial intelligence 
 
 Major goals 
 * Artificial general intelligence
 * Planning 
 * Computer vision 
 * General game playing 
 * Knowledge reasoning 
 * Machine learning 
 * Natural language processing 
 * Robotics 
 Approaches 
 * Symbolic 
 * Deep learning 
 * Bayesian networks 
 * Evolutionary algorithms 
 Philosophy 
 * Chinese room 
 * Friendly AI 
 * Control problem/Takeover 
 * Ethics 
 * Existential risk 
 * Turing test 
 History 
 * Timeline 
 * Progress 
 * AI winter 
 Technology 
 * Applications 
 * Projects 
 * Programming languages 
 Glossary 
 * Glossary 
 * v 
 * t 
 * e 
 

 Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks.[1] It is seen as a part of artificial intelligence.

 Machine learning algorithms build a model based on sample data, known as training data, in order to make predictions or decisions without being explicitly programmed to do so.[2] Machine learning algorithms are used in a wide variety of applications, such as in medicine, email filtering, speech recognition, agriculture, and computer vision, where it is difficult or unfeasible to develop conventional algorithms to perform the needed tasks.[3][4]

 A subset of machine learning is closely related to computational statistics, which focuses on making predictions using computers, but not all machine learning is statistical learning. The study of mathematical optimization delivers methods, theory and application domains to the field of machine learning. Data mining is a related field of study, focusing on exploratory data analysis through unsupervised learning.[6][7]

 Some implementations of machine learning use data and neural networks in a way that mimics the working of a biological brain.[8][9]

 In its application across business problems, machine learning is also referred to as predictive analytics.

 Overview [ edit ]

 Learning algorithms work on the basis that strategies, algorithms, and inferences that worked well in the past are likely to continue working well in the future. These inferences can be obvious, such as "since the sun rose every morning for the last 10,000 days, it will probably rise tomorrow morning as well". They can be nuanced, such as "X% of families have geographically separate species with color variants, so there is a Y% chance that undiscovered black swans exist".[10]

 Machine learning programs can perform tasks without being explicitly programmed to do so. It involves computers learning from data provided so that they carry out certain tasks. For simple tasks assigned to computers, it is possible to program algorithms telling the machine how to execute all steps required to solve the problem at hand; on the computer's part, no learning is needed. For more advanced tasks, it can be challenging for a human to manually create the needed algorithms. In practice, it can turn out to be more effective to help the machine develop its own algorithm, rather than having human programmers specify every needed step.[11]

 The discipline of machine learning employs various approaches to teach computers to accomplish tasks where no fully satisfactory algorithm is available. In cases where vast numbers of potential answers exist, one approach is to label some of the correct answers as valid. This can then be used as training data for the computer to improve the algorithm(s) it uses to determine correct answers. For example, to train a system for the task of digital character recognition, the MNIST dataset of handwritten digits has often been used.[11]

 History and relationships to other fields [ edit ]

 See also: Timeline of machine learning

 The term machine learning was coined in 1959 by Arthur Samuel, an IBM employee and pioneer in the field of computer gaming and artificial intelligence.[12][13] The synonym self-teaching computers was also used in this time period.[14][15]

 By the early 1960s an experimental "learning machine" with punched tape memory, called CyberTron, had been developed by Raytheon Company to analyze sonar signals, electrocardiograms, and speech patterns using rudimentary reinforcement learning. It was repetitively "trained" by a human operator/teacher to recognize patterns and equipped with a "goof" button to cause it to re-evaluate incorrect decisions.[16] A representative book on research into machine learning during the 1960s was Nilsson's book on Learning Machines, dealing mostly with machine learning for pattern classification.[17] Interest related to pattern recognition continued into the 1970s, as described by Duda and Hart in 1973.[18] In 1981 a report was given on using teaching strategies so that a neural network learns to recognize 40 characters (26 letters, 10 digits, and 4 special symbols) from a computer terminal.[19]

 Tom M. Mitchell provided a widely quoted, more formal definition of the algorithms studied in the machine learning field: "A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured by P, improves with experience E."[20] This definition of the tasks in which machine learning is concerned offers a fundamentally operational definition rather than defining the field in cognitive terms. This follows Alan Turing's proposal in his paper "Computing Machinery and Intelligence", in which the question "Can machines think?" is replaced with the question "Can machines do what we (as thinking entities) can do?".[21]

 Modern-day machine learning has two objectives, one is to classify data based on models which have been developed, the other purpose is to make predictions for future outcomes based on these models. A hypothetical algorithm specific to classifying data may use computer vision of moles coupled with supervised learning in order to train it to classify the cancerous moles. A machine learning algorithm for stock trading may inform the trader of future potential predictions.[22]

 Artificial intelligence [ edit ]

 Machine learning as subfield of AI[23]
 Part of machine learning as subfield of AI or part of AI as subfield of machine learning[24]

 As a scientific endeavor, machine learning grew out of the quest for artificial intelligence. In the early days of AI as an academic discipline, some researchers were interested in having machines learn from data. They attempted to approach the problem with various symbolic methods, as well as what was then termed "neural networks"; these were mostly perceptrons and other models that were later found to be reinventions of the generalized linear models of statistics.[25] Probabilistic reasoning was also employed, especially in automated medical diagnosis.[26] : 488

 However, an increasing emphasis on the logical, knowledge-based approach caused a rift between AI and machine learning. Probabilistic systems were plagued by theoretical and practical problems of data acquisition and representation.[26] : 488 By 1980, expert systems had come to dominate AI, and statistics was out of favor.[27] Work on symbolic/knowledge-based learning did continue within AI, leading to inductive logic programming, but the more statistical line of research was now outside the field of AI proper, in pattern recognition and information retrieval.[26] : 708–710, 755 Neural networks research had been abandoned by AI and computer science around the same time. This line, too, was continued outside the AI/CS field, as "connectionism", by researchers from other disciplines including Hopfield, Rumelhart, and Hinton. Their main success came in the mid-1980s with the reinvention of backpropagation.[26] : 25

 Machine learning (ML), reorganized as a separate field, started to flourish in the 1990s. The field changed its goal from achieving artificial intelligence to tackling solvable problems of a practical nature. It shifted focus away from the symbolic approaches it had inherited from AI, and toward methods and models borrowed from statistics, fuzzy logic, and probability theory.[27]

 The difference between ML and AI is frequently misunderstood. ML learns and predicts based on passive observations, whereas AI implies an agent interacting with the environment to learn and take actions that maximize its chance of successfully achieving its goals.[28]

 As of 2020, many sources continue to assert that ML remains a subfield of AI.[29][30][27] Others have the view that not all ML is part of AI, but only an 'intelligent subset' of ML should be considered AI.[5][31][32]

 Data mining [ edit ]

 Machine learning and data mining often employ the same methods and overlap significantly, but while machine learning focuses on prediction, based on known properties learned from the training data, data mining focuses on the discovery of (previously) unknown properties in the data (this is the analysis step of knowledge discovery in databases). Data mining uses many machine learning methods, but with different goals; on the other hand, machine learning also employs data mining methods as "unsupervised learning" or as a preprocessing step to improve learner accuracy. Much of the confusion between these two research communities (which do often have separate conferences and separate journals, ECML PKDD being a major exception) comes from the basic assumptions they work with: in machine learning, performance is usually evaluated with respect to the ability to reproduce known knowledge, while in knowledge discovery and data mining (KDD) the key task is the discovery of previously unknown knowledge. Evaluated with respect to known knowledge, an uninformed (unsupervised) method will easily be outperformed by other supervised methods, while in a typical KDD task, supervised methods cannot be used due to the unavailability of training data.

 Optimization [ edit ]

 Machine learning also has intimate ties to optimization: many learning problems are formulated as minimization of some loss function on a training set of examples. Loss functions express the discrepancy between the predictions of the model being trained and the actual problem instances (for example, in classification, one wants to assign a label to instances, and models are trained to correctly predict the pre-assigned labels of a set of examples).[33]

 Generalization [ edit ]

 The difference between optimization and machine learning arises from the goal of generalization: while optimization algorithms can minimize the loss on a training set, machine learning is concerned with minimizing the loss on unseen samples. Characterizing the generalization of various learning algorithms is an active topic of current research, especially for deep learning algorithms.

 Statistics [ edit ]

 Machine learning and statistics are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population inferences from a sample, while machine learning finds generalizable predictive patterns.[34] According to Michael I. Jordan, the ideas of machine learning, from methodological principles to theoretical tools, have had a long pre-history in statistics.[35] He also suggested the term data science as a placeholder to call the overall field.[35]

 Leo Breiman distinguished two statistical modeling paradigms: data model and algorithmic model,[29] wherein "algorithmic model" means more or less the machine learning algorithms like Random Forest.

 Some statisticians have adopted methods from machine learning, leading to a combined field that they call statistical learning.[30]

 Physics [ edit ]

 Analytical and computational techniques derived from statistical physics of disordered systems, can be extended to large-scale problems, including machine learning, e.g., to analyze the weight space of deep neural networks.[36] Statistical physics is thus finding applications in the area of medical diagnostics.[37]

 Theory [ edit ]

 Main articles: Computational learning theory and Statistical learning theory

 A core objective of a learner is to generalize from its experience.[5][31] Generalization in this context is the ability of a learning machine to perform accurately on new, unseen examples/tasks after having experienced a learning data set. The training examples come from some generally unknown probability distribution (considered representative of the space of occurrences) and the learner has to build a general model about this space that enables it to produce sufficiently accurate predictions in new cases.

 The computational analysis of machine learning algorithms and their performance is a branch of theoretical computer science known as computational learning theory via the Probably Approximately Correct Learning (PAC) model. Because training sets are finite and the future is uncertain, learning theory usually does not yield guarantees of the performance of algorithms. Instead, probabilistic bounds on the performance are quite common. The bias–variance decomposition is one way to quantify generalization error.

 For the best performance in the context of generalization, the complexity of the hypothesis should match the complexity of the function underlying the data. If the hypothesis is less complex than the function, then the model has under fitted the data. If the complexity of the model is increased in response, then the training error decreases. But if the hypothesis is too complex, then the model is subject to overfitting and generalization will be poorer.[32]

 In addition to performance bounds, learning theorists study the time complexity and feasibility of learning. In computational learning theory, a computation is considered feasible if it can be done in polynomial time. There are two kinds of time complexity results: Positive results show that a certain class of functions can be learned in polynomial time. Negative results show that certain classes cannot be learned in polynomial time.

 Approaches [ edit ]

 Machine learning approaches are traditionally divided into three broad categories, which correspond to learning paradigms, depending on the nature of the "signal" or "feedback" available to the learning system:

 * Supervised learning: The computer is presented with example inputs and their desired outputs, given by a "teacher", and the goal is to learn a general rule that maps inputs to outputs.
 * Unsupervised learning: No labels are given to the learning algorithm, leaving it on its own to find structure in its input. Unsupervised learning can be a goal in itself (discovering hidden patterns in data) or a means towards an end (feature learning).
 * Reinforcement learning: A computer program interacts with a dynamic environment in which it must perform a certain goal (such as driving a vehicle or playing a game against an opponent). As it navigates its problem space, the program is provided feedback that's analogous to rewards, which it tries to maximize.[5]

 Supervised learning [ edit ]

 Main article: Supervised learning
 A support-vector machine is a supervised learning model that divides the data into regions separated by a linear boundary. Here, the linear boundary divides the black circles from the white.

 Supervised learning algorithms build a mathematical model of a set of data that contains both the inputs and the desired outputs.[38] The data is known as training data, and consists of a set of training examples. Each training example has one or more inputs and the desired output, also known as a supervisory signal. In the mathematical model, each training example is represented by an array or vector, sometimes called a feature vector, and the training data is represented by a matrix. Through iterative optimization of an objective function, supervised learning algorithms learn a function that can be used to predict the output associated with new inputs.[39] An optimal function will allow the algorithm to correctly determine the output for inputs that were not a part of the training data. An algorithm that improves the accuracy of its outputs or predictions over time is said to have learned to perform that task.[20]

 Types of supervised-learning algorithms include active learning, classification and regression.[28] Classification algorithms are used when the outputs are restricted to a limited set of values, and regression algorithms are used when the outputs may have any numerical value within a range. As an example, for a classification algorithm that filters emails, the input would be an incoming email, and the output would be the name of the folder in which to file the email.

 Similarity learning is an area of supervised machine learning closely related to regression and classification, but the goal is to learn from examples using a similarity function that measures how similar or related two objects are. It has applications in ranking, recommendation systems, visual identity tracking, face verification, and speaker verification.

 Unsupervised learning [ edit ]

 Main article: Unsupervised learning
 See also: Cluster analysis

 Unsupervised learning algorithms take a set of data that contains only inputs, and find structure in the data, like grouping or clustering of data points. The algorithms, therefore, learn from test data that has not been labeled, classified or categorized. Instead of responding to feedback, unsupervised learning algorithms identify commonalities in the data and react based on the presence or absence of such commonalities in each new piece of data. A central application of unsupervised learning is in the field of density estimation in statistics, such as finding the probability density function.[40] Though unsupervised learning encompasses other domains involving summarizing and explaining data features.

 Cluster analysis is the assignment of a set of observations into subsets (called clusters) so that observations within the same cluster are similar according to one or more predesignated criteria, while observations drawn from different clusters are dissimilar. Different clustering techniques make different assumptions on the structure of the data, often defined by some similarity metric and evaluated, for example, by internal compactness, or the similarity between members of the same cluster, and separation, the difference between clusters. Other methods are based on estimated density and graph connectivity.

 Semi-supervised learning [ edit ]

 Main article: Semi-supervised learning

 Semi-supervised learning falls between unsupervised learning (without any labeled training data) and supervised learning (with completely labeled training data). Some of the training examples are missing training labels, yet many machine-learning researchers have found that unlabeled data, when used in conjunction with a small amount of labeled data, can produce a considerable improvement in learning accuracy.

 In weakly supervised learning, the training labels are noisy, limited, or imprecise; however, these labels are often cheaper to obtain, resulting in larger effective training sets.[41]

 Reinforcement learning [ edit ]

 Main article: Reinforcement learning

 Reinforcement learning is an area of machine learning concerned with how software agents ought to take actions in an environment so as to maximize some notion of cumulative reward. Due to its generality, the field is studied in many other disciplines, such as game theory, control theory, operations research, information theory, simulation-based optimization, multi-agent systems, swarm intelligence, statistics and genetic algorithms. In machine learning, the environment is typically represented as a Markov decision process (MDP). Many reinforcements learning algorithms use dynamic programming techniques.[42] Reinforcement learning algorithms do not assume knowledge of an exact mathematical model of the MDP and are used when exact models are infeasible. Reinforcement learning algorithms are used in autonomous vehicles or in learning to play a game against a human opponent.

 Dimensionality reduction [ edit ]

 Dimensionality reduction is a process of reducing the number of random variables under consideration by obtaining a set of principal variables.[43] In other words, it is a process of reducing the dimension of the feature set, also called the "number of features". Most of the dimensionality reduction techniques can be considered as either feature elimination or extraction. One of the popular methods of dimensionality reduction is principal component analysis (PCA). PCA involves changing higher-dimensional data (e.g., 3D) to a smaller space (e.g., 2D). This results in a smaller dimension of data (2D instead of 3D), while keeping all original variables in the model without changing the data.[44] The manifold hypothesis proposes that high-dimensional data sets lie along low-dimensional manifolds, and many dimensionality reduction techniques make this assumption, leading to the area of manifold learning and manifold regularization.

 Other types [ edit ]

 Other approaches have been developed which don't fit neatly into this three-fold categorization, and sometimes more than one is used by the same machine learning system. For example, topic modeling, meta-learning.[45]

 As of 2022, deep learning is the dominant approach for much ongoing work in the field of machine learning.[11]

 Self-learning [ edit ]

 Self-learning, as a machine learning paradigm was introduced in 1982 along with a neural network capable of self-learning, named crossbar adaptive array (CAA).[46] It is learning with no external rewards and no external teacher advice. The CAA self-learning algorithm computes, in a crossbar fashion, both decisions about actions and emotions (feelings) about consequence situations. The system is driven by the interaction between cognition and emotion.[47] The self-learning algorithm updates a memory matrix W =||w(a,s)|| such that in each iteration executes the following machine learning routine:

 1. in situation s perform action a
 2. receive consequence situation s'
 3. compute emotion of being in consequence situation v(s')
 4. update crossbar memory w'(a,s) = w(a,s) + v(s')

 It is a system with only one input, situation, and only one output, action (or behavior) a. There is neither a separate reinforcement input nor an advice input from the environment. The backpropagated value (secondary reinforcement) is the emotion toward the consequence situation. The CAA exists in two environments, one is the behavioral environment where it behaves, and the other is the genetic environment, wherefrom it initially and only once receives initial emotions about situations to be encountered in the behavioral environment. After receiving the genome (species) vector from the genetic environment, the CAA learns a goal-seeking behavior, in an environment that contains both desirable and undesirable situations.[48]

 Feature learning [ edit ]

 Main article: Feature learning

 Several learning algorithms aim at discovering better representations of the inputs provided during training.[49] Classic examples include principal component analysis and cluster analysis. Feature learning algorithms, also called representation learning algorithms, often attempt to preserve the information in their input but also transform it in a way that makes it useful, often as a pre-processing step before performing classification or predictions. This technique allows reconstruction of the inputs coming from the unknown data-generating distribution, while not being necessarily faithful to configurations that are implausible under that distribution. This replaces manual feature engineering, and allows a machine to both learn the features and use them to perform a specific task.

 Feature learning can be either supervised or unsupervised. In supervised feature learning, features are learned using labeled input data. Examples include artificial neural networks, multilayer perceptrons, and supervised dictionary learning. In unsupervised feature learning, features are learned with unlabeled input data. Examples include dictionary learning, independent component analysis, autoencoders, matrix factorization[50] and various forms of clustering.[51][52][53]

 Manifold learning algorithms attempt to do so under the constraint that the learned representation is low-dimensional. Sparse coding algorithms attempt to do so under the constraint that the learned representation is sparse, meaning that the mathematical model has many zeros. Multilinear subspace learning algorithms aim to learn low-dimensional representations directly from tensor representations for multidimensional data, without reshaping them into higher-dimensional vectors.[54] Deep learning algorithms discover multiple levels of representation, or a hierarchy of features, with higher-level, more abstract features defined in terms of (or generating) lower-level features. It has been argued that an intelligent machine is one that learns a representation that disentangles the underlying factors of variation that explain the observed data.[55]

 Feature learning is motivated by the fact that machine learning tasks such as classification often require input that is mathematically and computationally convenient to process. However, real-world data such as images, video, and sensory data has not yielded attempts to algorithmically define specific features. An alternative is to discover such features or representations through examination, without relying on explicit algorithms.

 Sparse dictionary learning [ edit ]

 Main article: Sparse dictionary learning

 Sparse dictionary learning is a feature learning method where a training example is represented as a linear combination of basis functions, and is assumed to be a sparse matrix. The method is strongly NP-hard and difficult to solve approximately.[56] A popular heuristic method for sparse dictionary learning is the K-SVD algorithm. Sparse dictionary learning has been applied in several contexts. In classification, the problem is to determine the class to which a previously unseen training example belongs. For a dictionary where each class has already been built, a new training example is associated with the class that is best sparsely represented by the corresponding dictionary. Sparse dictionary learning has also been applied in image de-noising. The key idea is that a clean image patch can be sparsely represented by an image dictionary, but the noise cannot.[57]

 Anomaly detection [ edit ]

 Main article: Anomaly detection

 In data mining, anomaly detection, also known as outlier detection, is the identification of rare items, events or observations which raise suspicions by differing significantly from the majority of the data.[58] Typically, the anomalous items represent an issue such as bank fraud, a structural defect, medical problems or errors in a text. Anomalies are referred to as outliers, novelties, noise, deviations and exceptions.[59]

 In particular, in the context of abuse and network intrusion detection, the interesting objects are often not rare objects, but unexpected bursts of inactivity. This pattern does not adhere to the common statistical definition of an outlier as a rare object. Many outlier detection methods (in particular, unsupervised algorithms) will fail on such data unless aggregated appropriately. Instead, a cluster analysis algorithm may be able to detect the micro-clusters formed by these patterns.[60]

 Three broad categories of anomaly detection techniques exist.[61] Unsupervised anomaly detection techniques detect anomalies in an unlabeled test data set under the assumption that the majority of the instances in the data set are normal, by looking for instances that seem to fit the least to the remainder of the data set. Supervised anomaly detection techniques require a data set that has been labeled as "normal" and "abnormal" and involves training a classifier (the key difference to many other statistical classification problems is the inherently unbalanced nature of outlier detection). Semi-supervised anomaly detection techniques construct a model representing normal behavior from a given normal training data set and then test the likelihood of a test instance to be generated by the model.

 Robot learning [ edit ]

 Robot learning is inspired by a multitude of machine learning methods, starting from supervised learning, reinforcement learning,[62][63] and finally meta-learning (e.g. MAML).

 Association rules [ edit ]

 Main article: Association rule learning
 See also: Inductive logic programming

 Association rule learning is a rule-based machine learning method for discovering relationships between variables in large databases. It is intended to identify strong rules discovered in databases using some measure of "interestingness".[64]

 Rule-based machine learning is a general term for any machine learning method that identifies, learns, or evolves "rules" to store, manipulate or apply knowledge. The defining characteristic of a rule-based machine learning algorithm is the identification and utilization of a set of relational rules that collectively represent the knowledge captured by the system. This is in contrast to other machine learning algorithms that commonly identify a singular model that can be universally applied to any instance in order to make a prediction.[65] Rule-based machine learning approaches include learning classifier systems, association rule learning, and artificial immune systems.

 Based on the concept of strong rules, Rakesh Agrawal, Tomasz Imieliński and Arun Swami introduced association rules for discovering regularities between products in large-scale transaction data recorded by point-of-sale (POS) systems in supermarkets.[66] For example, the rule found in the sales data of a supermarket would indicate that if a customer buys onions and potatoes together, they are likely to also buy hamburger meat. Such information can be used as the basis for decisions about marketing activities such as promotional pricing or product placements. In addition to market basket analysis, association rules are employed today in application areas including Web usage mining, intrusion detection, continuous production, and bioinformatics. In contrast with sequence mining, association rule learning typically does not consider the order of items either within a transaction or across transactions.

 Learning classifier systems (LCS) are a family of rule-based machine learning algorithms that combine a discovery component, typically a genetic algorithm, with a learning component, performing either supervised learning, reinforcement learning, or unsupervised learning. They seek to identify a set of context-dependent rules that collectively store and apply knowledge in a piecewise manner in order to make predictions.[67]

 Inductive logic programming (ILP) is an approach to rule learning using logic programming as a uniform representation for input examples, background knowledge, and hypotheses. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesized logic program that entails all positive and no negative examples. Inductive programming is a related field that considers any kind of programming language for representing hypotheses (and not only logic programming), such as functional programs.

 Inductive logic programming is particularly useful in bioinformatics and natural language processing. Gordon Plotkin and Ehud Shapiro laid the initial theoretical foundation for inductive machine learning in a logical setting.[68][69][70] Shapiro built their first implementation (Model Inference System) in 1981: a Prolog program that inductively inferred logic programs from positive and negative examples.[71] The term inductive here refers to philosophical induction, suggesting a theory to explain observed facts, rather than mathematical induction, proving a property for all members of a well-ordered set.

 Models [ edit ]

 Performing machine learning involves creating a model, which is trained on some training data and then can process additional data to make predictions. Various types of models have been used and researched for machine learning systems.

 Artificial neural networks [ edit ]

 Main article: Artificial neural network
 See also: Deep learning
 An artificial neural network is an interconnected group of nodes, akin to the vast network of neurons in a brain. Here, each circular node represents an artificial neuron and an arrow represents a connection from the output of one artificial neuron to the input of another.

 Artificial neural networks (ANNs), or connectionist systems, are computing systems vaguely inspired by the biological neural networks that constitute animal brains. Such systems "learn" to perform tasks by considering examples, generally without being programmed with any task-specific rules.

 An ANN is a model based on a collection of connected units or nodes called "artificial neurons", which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit information, a "signal", from one artificial neuron to another. An artificial neuron that receives a signal can process it and then signal additional artificial neurons connected to it. In common ANN implementations, the signal at a connection between artificial neurons is a real number, and the output of each artificial neuron is computed by some non-linear function of the sum of its inputs. The connections between artificial neurons are called "edges". Artificial neurons and edges typically have a weight that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Artificial neurons may have a threshold such that the signal is only sent if the aggregate signal crosses that threshold. Typically, artificial neurons are aggregated into layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first layer (the input layer) to the last layer (the output layer), possibly after traversing the layers multiple times.

 The original goal of the ANN approach was to solve problems in the same way that a human brain would. However, over time, attention moved to performing specific tasks, leading to deviations from biology. Artificial neural networks have been used on a variety of tasks, including computer vision, speech recognition, machine translation, social network filtering, playing board and video games and medical diagnosis.

 Deep learning consists of multiple hidden layers in an artificial neural network. This approach tries to model the way the human brain processes light and sound into vision and hearing. Some successful applications of deep learning are computer vision and speech recognition.[72]

 Decision trees [ edit ]

 Main article: Decision tree learning
 A decision tree showing survival probability of passengers on the Titanic

 Decision tree learning uses a decision tree as a predictive model to go from observations about an item (represented in the branches) to conclusions about the item's target value (represented in the leaves). It is one of the predictive modeling approaches used in statistics, data mining, and machine learning. Tree models where the target variable can take a discrete set of values are called classification trees; in these tree structures, leaves represent class labels, and branches represent conjunctions of features that lead to those class labels. Decision trees where the target variable can take continuous values (typically real numbers) are called regression trees. In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making. In data mining, a decision tree describes data, but the resulting classification tree can be an input for decision-making.

 Support-vector machines [ edit ]

 Main article: Support-vector machine

 Support-vector machines (SVMs), also known as support-vector networks, are a set of related supervised learning methods used for classification and regression. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that predicts whether a new example falls into one category.[73] An SVM training algorithm is a non-probabilistic, binary, linear classifier, although methods such as Platt scaling exist to use SVM in a probabilistic classification setting. In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces.

 Regression analysis [ edit ]

 Main article: Regression analysis
 Illustration of linear regression on a data set

 Regression analysis encompasses a large variety of statistical methods to estimate the relationship between input variables and their associated features. Its most common form is linear regression, where a single line is drawn to best fit the given data according to a mathematical criterion such as ordinary least squares. The latter is often extended by regularization methods to mitigate overfitting and bias, as in ridge regression. When dealing with non-linear problems, go-to models include polynomial regression (for example, used for trendline fitting in Microsoft Excel[74]), logistic regression (often used in statistical classification) or even kernel regression, which introduces non-linearity by taking advantage of the kernel trick to implicitly map input variables to higher-dimensional space.

 Bayesian networks [ edit ]

 Main article: Bayesian network
 A simple Bayesian network. Rain influences whether the sprinkler is activated, and both rain and the sprinkler influence whether the grass is wet.

 A Bayesian network, belief network, or directed acyclic graphical model is a probabilistic graphical model that represents a set of random variables and their conditional independence with a directed acyclic graph (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms exist that perform inference and learning. Bayesian networks that model sequences of variables, like speech signals or protein sequences, are called dynamic Bayesian networks. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty are called influence diagrams.

 Gaussian processes [ edit ]

 Main article: Gaussian processes
 An example of Gaussian Process Regression (prediction) compared with other regression models[75]

 A Gaussian process is a stochastic process in which every finite collection of the random variables in the process has a multivariate normal distribution, and it relies on a pre-defined covariance function, or kernel, that models how pairs of points relate to each other depending on their locations.

 Given a set of observed points, or input–output examples, the distribution of the (unobserved) output of a new point as function of its input data, can be directly computed by looking like the observed points and the covariances between those points and the new, unobserved point.

 Gaussian processes are popular surrogate models in Bayesian optimization used to do hyperparameter optimization.

 Genetic algorithms [ edit ]

 Main article: Genetic algorithm

 A genetic algorithm (GA) is a search algorithm and heuristic technique that mimics the process of natural selection, using methods such as mutation and crossover to generate new genotypes in the hope of finding good solutions to a given problem. In machine learning, genetic algorithms were used in the 1980s and 1990s.[76][77] Conversely, machine learning techniques have been used to improve the performance of genetic and evolutionary algorithms.[78]

 Training models [ edit ]

 Typically, machine learning models require a high quantity of reliable data in order for the models to perform accurate predictions. When training a machine learning model, machine learning engineers need to target and collect a large and representative sample of data. Data from the training set can be as varied as a corpus of text, a collection of images, sensor data, and data collected from individual users of a service. Overfitting is something to watch out for when training a machine learning model. Trained models derived from biased or non-evaluated data can result in skewed or undesired predictions. Bias models may result in detrimental outcomes thereby furthering the negative impacts on society or objectives. Algorithmic bias is a potential result of data not being fully prepared for training. Machine learning ethics is becoming a field of study and notably be integrated within machine learning engineering teams.

 Federated learning [ edit ]

 Main article: Federated learning

 Federated learning is an adapted form of distributed artificial intelligence to training machine learning models that decentralizes the training process, allowing for users' privacy to be maintained by not needing to send their data to a centralized server. This also increases efficiency by decentralizing the training process to many devices. For example, Gboard uses federated machine learning to train search query prediction models on users' mobile phones without having to send individual searches back to Google.[79]

 Applications [ edit ]

 There are many applications for machine learning, including:

 * Agriculture
 * Anatomy
 * Adaptive website
 * Affective computing
 * Astronomy
 * Automated decision-making
 * Banking
 * Behaviorism
 * Bioinformatics
 * Brain–machine interfaces
 * Cheminformatics
 * Citizen Science
 * Climate Science
 * Computer networks
 * Computer vision
 * Credit-card fraud detection
 * Data quality
 * DNA sequence classification
 * Economics
 * Financial market analysis[80]
 * General game playing
 * Handwriting recognition
 * Information retrieval
 * Insurance
 * Internet fraud detection
 * Knowledge graph embedding
 * Linguistics
 * Machine learning control
 * Machine perception
 * Machine translation
 * Marketing
 * Medical diagnosis
 * Natural language processing
 * Natural language understanding
 * Online advertising
 * Optimization
 * Recommender systems
 * Robot locomotion
 * Search engines
 * Sentiment analysis
 * Sequence mining
 * Software engineering
 * Speech recognition
 * Structural health monitoring
 * Syntactic pattern recognition
 * Telecommunication
 * Theorem proving
 * Time-series forecasting
 * User behavior analytics

 In 2006, the media-services provider Netflix held the first "Netflix Prize" competition to find a program to better predict user preferences and improve the accuracy of its existing Cinematch movie recommendation algorithm by at least 10%. A joint team made up of researchers from AT&T Labs-Research in collaboration with the teams Big Chaos and Pragmatic Theory built an ensemble model to win the Grand Prize in 2009 for $1 million.[81] Shortly after the prize was awarded, Netflix realized that viewers' ratings were not the best indicators of their viewing patterns ("everything is a recommendation") and they changed their recommendation engine accordingly.[82] In 2010 The Wall Street Journal wrote about the firm Rebellion Research and their use of machine learning to predict the financial crisis.[83] In 2012, co-founder of Sun Microsystems, Vinod Khosla, predicted that 80% of medical doctors jobs would be lost in the next two decades to automated machine learning medical diagnostic software.[84] In 2014, it was reported that a machine learning algorithm had been applied in the field of art history to study fine art paintings and that it may have revealed previously unrecognized influences among artists.[85] In 2019 Springer Nature published the first research book created using machine learning.[86] In 2020, machine learning technology was used to help make diagnoses and aid researchers in developing a cure for COVID-19.[87] Machine learning was recently applied to predict the pro-environmental behavior of travelers.[88] Recently, machine learning technology was also applied to optimize smartphone's performance and thermal behavior based on the user's interaction with the phone.[89][90][91]

 Limitations [ edit ]

 Although machine learning has been transformative in some fields, machine-learning programs often fail to deliver expected results.[92][93][94] Reasons for this are numerous: lack of (suitable) data, lack of access to the data, data bias, privacy problems, badly chosen tasks and algorithms, wrong tools and people, lack of resources, and evaluation problems.[95]

 In 2018, a self-driving car from Uber failed to detect a pedestrian, who was killed after a collision.[96] Attempts to use machine learning in healthcare with the IBM Watson system failed to deliver even after years of time and billions of dollars invested.[97][98]

 Machine learning has been used as a strategy to update the evidence related to a systematic review and increased reviewer burden related to the growth of biomedical literature. While it has improved with training sets, it has not yet developed sufficiently to reduce the workload burden without limiting the necessary sensitivity for the findings research themselves.[99]

 Bias [ edit ]

 Main article: Algorithmic bias

 Machine learning approaches in particular can suffer from different data biases. A machine learning system trained specifically on current customers may not be able to predict the needs of new customer groups that are not represented in the training data. When trained on man-made data, machine learning is likely to pick up the constitutional and unconscious biases already present in society.[100] Language models learned from data have been shown to contain human-like biases.[101][102] Machine learning systems used for criminal risk assessment have been found to be biased against black people.[103][104] In 2015, Google photos would often tag black people as gorillas,[105] and in 2018 this still was not well resolved, but Google reportedly was still using the workaround to remove all gorillas from the training data, and thus was not able to recognize real gorillas at all.[106] Similar issues with recognizing non-white people have been found in many other systems.[107] In 2016, Microsoft tested a chatbot that learned from Twitter, and it quickly picked up racist and sexist language.[108] Because of such challenges, the effective use of machine learning may take longer to be adopted in other domains.[109] Concern for fairness in machine learning, that is, reducing bias in machine learning and propelling its use for human good is increasingly expressed by artificial intelligence scientists, including Fei-Fei Li, who reminds engineers that "There's nothing artificial about AI...It's inspired by people, it's created by people, and—most importantly—it impacts people. It is a powerful tool we are only just beginning to understand, and that is a profound responsibility."[110]

 Explainability [ edit ]

 Main article: Explainable artificial intelligence

 Explainable AI (XAI), or Interpretable AI, or Explainable Machine Learning (XML), is artificial intelligence (AI) in which humans can understand the decisions or predictions made by the AI. It contrasts with the "black box" concept in machine learning where even its designers cannot explain why an AI arrived at a specific decision. By refining the mental models of users of AI-powered systems and dismantling their misconceptions, XAI promises to help users perform more effectively. XAI may be an implementation of the social right to explanation.

 Overfitting [ edit ]

 Main article: Overfitting
 The blue line could be an example of overfitting a linear function due to random noise.

 Settling on a bad, overly complex theory gerrymandered to fit all the past training data is known as overfitting. Many systems attempt to reduce overfitting by rewarding a theory in accordance with how well it fits the data but penalizing the theory in accordance with how complex the theory is.[10]

 Other limitations and vulnerabilities [ edit ]

 Learners can also disappoint by "learning the wrong lesson". A toy example is that an image classifier trained only on pictures of brown horses and black cats might conclude that all brown patches are likely to be horses.[111] A real-world example is that, unlike humans, current image classifiers often don't primarily make judgments from the spatial relationship between components of the picture, and they learn relationships between pixels that humans are oblivious to, but that still correlate with images of certain types of real objects. Modifying these patterns on a legitimate image can result in "adversarial" images that the system misclassifies.[112][113]

 Adversarial vulnerabilities can also result in nonlinear systems, or from non-pattern perturbations. Some systems are so brittle that changing a single adversarial pixel predictably induces misclassification.[ citation needed ] Machine learning models are often vulnerable to manipulation and/or evasion via adversarial machine learning.[114]

 Researchers have demonstrated how backdoors can be placed undetectably into classifying (e.g., for categories "spam" and well-visible "not spam" of posts) machine learning models which are often developed and/or trained by third parties. Parties can change the classification of any input, including in cases for which a type of data/software transparency is provided, possibly including white-box access.[115][116][117]

 Model assessments [ edit ]

 Classification of machine learning models can be validated by accuracy estimation techniques like the holdout method, which splits the data in a training and test set (conventionally 2/3 training set and 1/3 test set designation) and evaluates the performance of the training model on the test set. In comparison, the K-fold-cross-validation method randomly partitions the data into K subsets and then K experiments are performed each respectively considering 1 subset for evaluation and the remaining K-1 subsets for training the model. In addition to the holdout and cross-validation methods, bootstrap, which samples n instances with replacement from the dataset, can be used to assess model accuracy.[118]

 In addition to overall accuracy, investigators frequently report sensitivity and specificity meaning True Positive Rate (TPR) and True Negative Rate (TNR) respectively. Similarly, investigators sometimes report the false positive rate (FPR) as well as the false negative rate (FNR). However, these rates are ratios that fail to reveal their numerators and denominators. The total operating characteristic (TOC) is an effective method to express a model's diagnostic ability. TOC shows the numerators and denominators of the previously mentioned rates, thus TOC provides more information than the commonly used receiver operating characteristic (ROC) and ROC's associated area under the curve (AUC).[119]

 Ethics [ edit ]

 See also: AI control problem and Toronto Declaration

 Machine learning poses a host of ethical questions. Systems that are trained on datasets collected with biases may exhibit these biases upon use (algorithmic bias), thus digitizing cultural prejudices.[120] For example, in 1988, the UK's Commission for Racial Equality found that St. George's Medical School had been using a computer program trained from data of previous admissions staff and this program had denied nearly 60 candidates who were found to be either women or had non-European sounding names.[100] Using job hiring data from a firm with racist hiring policies may lead to a machine learning system duplicating the bias by scoring job applicants by similarity to previous successful applicants.[121][122] Responsible collection of data and documentation of algorithmic rules used by a system thus is a critical part of machine learning.

 AI can be well-equipped to make decisions in technical fields, which rely heavily on data and historical information. These decisions rely on the objectivity and logical reasoning.[123] Because human languages contain biases, machines trained on language corpora will necessarily also learn these biases.[124][125]

 Other forms of ethical challenges, not related to personal biases, are seen in health care. There are concerns among health care professionals that these systems might not be designed in the public's interest but as income-generating machines.[126] This is especially true in the United States where there is a long-standing ethical dilemma of improving health care, but also increase profits. For example, the algorithms could be designed to provide patients with unnecessary tests or medication in which the algorithm's proprietary owners hold stakes. There is potential for machine learning in health care to provide professionals an additional tool to diagnose, medicate, and plan recovery paths for patients, but this requires these biases to be mitigated.[127]

 Hardware [ edit ]

 Since the 2010s, advances in both machine learning algorithms and computer hardware have led to more efficient methods for training deep neural networks (a particular narrow subdomain of machine learning) that contain many layers of non-linear hidden units.[128] By 2019, graphic processing units (GPUs), often with AI-specific enhancements, had displaced CPUs as the dominant method of training large-scale commercial cloud AI.[129] OpenAI estimated the hardware computing used in the largest deep learning projects from AlexNet (2012) to AlphaZero (2017), and found a 300,000-fold increase in the amount of compute required, with a doubling-time trendline of 3.4 months.[130][131]

 Neuromorphic/Physical Neural Networks [ edit ]

 A physical neural network or Neuromorphic computer is a type of artificial neural network in which an electrically adjustable material is used to emulate the function of a neural synapse. "Physical" neural network is used to emphasize the reliance on physical hardware used to emulate neurons as opposed to software-based approaches. More generally the term is applicable to other artificial neural networks in which a memristor or other electrically adjustable resistance material is used to emulate a neural synapse.[132][133]

 Embedded Machine Learning [ edit ]

 Embedded Machine Learning is a sub-field of machine learning, where the machine learning model is run on embedded systems with limited computing resources such as wearable computers, edge devices and microcontrollers.[134][135][136] Running machine learning model in embedded devices removes the need for transferring and storing data on cloud servers for further processing, henceforth, reducing data breaches and privacy leaks happening because of transferring data, and also minimizes theft of intellectual properties, personal data and business secrets. Embedded Machine Learning could be applied through several techniques including hardware acceleration,[137][138] using approximate computing,[139] optimization of machine learning models and many more.[140][141]

 Software [ edit ]

 Software suites containing a variety of machine learning algorithms include the following:

 Free and open-source software [ edit ]

 * Caffe
 * Deeplearning4j
 * DeepSpeed
 * ELKI
 * Google JAX
 * Infer.NET
 * Keras
 * Kubeflow
 * LightGBM
 * Mahout
 * Mallet
 * Microsoft Cognitive Toolkit
 * ML.NET
 * mlpack
 * MLFlow
 * MXNet
 * Neural Lab
 * OpenNN
 * Orange
 * pandas (software)
 * ROOT (TMVA with ROOT)
 * scikit-learn
 * Shogun
 * Spark MLlib
 * SystemML
 * TensorFlow
 * Torch / PyTorch
 * Weka / MOA
 * XGBoost
 * Yooreeka

 Proprietary software with free and open-source editions [ edit ]

 * KNIME
 * RapidMiner

 Proprietary software [ edit ]

 * Amazon Machine Learning
 * Angoss KnowledgeSTUDIO
 * Azure Machine Learning
 * Ayasdi
 * IBM Watson Studio
 * Google Cloud Vertex AI
 * Google Prediction API
 * IBM SPSS Modeler
 * KXEN Modeler
 * LIONsolver
 * Mathematica
 * MATLAB
 * Neural Designer
 * NeuroSolutions
 * Oracle Data Mining
 * Oracle AI Platform Cloud Service
 * PolyAnalyst
 * RCASE
 * SAS Enterprise Miner
 * SequenceL
 * Splunk
 * STATISTICA Data Miner

 Journals [ edit ]

 * Journal of Machine Learning Research
 * Machine Learning
 * Nature Machine Intelligence
 * Neural Computation
 * IEEE Transactions on Pattern Analysis and Machine Intelligence

 Conferences [ edit ]

 * AAAI Conference on Artificial Intelligence
 * Association for Computational Linguistics (ACL)
 * European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD)
 * International Conference on Computational Intelligence Methods for Bioinformatics and Biostatistics (CIBB)
 * International Conference on Machine Learning (ICML)
 * International Conference on Learning Representations (ICLR)
 * International Conference on Intelligent Robots and Systems (IROS)
 * Conference on Knowledge Discovery and Data Mining (KDD)
 * Conference on Neural Information Processing Systems (NeurIPS)

 See also [ edit ]

 * Automated machine learning – Process of automating the application of machine learning
 * Big data – Information assets characterized by high volume, velocity, and variety
 * Differentiable programming – Programming paradigm
 * List of important publications in machine learning
 * List of datasets for machine-learning research

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 Sources [ edit ]

 * Domingos, Pedro (September 22, 2015). The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World. Basic Books. ISBN 978-0465065707.
 * Nilsson, Nils (1998). Artificial Intelligence: A New Synthesis. Morgan Kaufmann. ISBN 978-1-55860-467-4. Archived from the original on 26 July 2020 . Retrieved 18 November 2019 .
 * Russell, Stuart J.; Norvig, Peter (2003), Artificial Intelligence: A Modern Approach (2nd ed.), Upper Saddle River, New Jersey: Prentice Hall, ISBN 0-13-790395-2.
 * Poole, David; Mackworth, Alan; Goebel, Randy (1998). Computational Intelligence: A Logical Approach. New York: Oxford University Press. ISBN 978-0-19-510270-3. Archived from the original on 26 July 2020 . Retrieved 22 August 2020 .

 Further reading [ edit ]

 * Nils J. Nilsson, Introduction to Machine Learning Archived 2019-08-16 at the Wayback Machine.
 * Trevor Hastie, Robert Tibshirani and Jerome H. Friedman (2001). The Elements of Statistical Learning Archived 2013-10-27 at the Wayback Machine, Springer. ISBN 0-387-95284-5.
 * Pedro Domingos (September 2015), The Master Algorithm, Basic Books, ISBN 978-0-465-06570-7
 * Ian H. Witten and Eibe Frank (2011). Data Mining: Practical machine learning tools and techniques Morgan Kaufmann, 664pp., ISBN 978-0-12-374856-0.
 * Ethem Alpaydin (2004). Introduction to Machine Learning, MIT Press, ISBN 978-0-262-01243-0.
 * David J. C. MacKay. Information Theory, Inference, and Learning Algorithms Archived 2016-02-17 at the Wayback Machine Cambridge: Cambridge University Press, 2003. ISBN 0-521-64298-1
 * Richard O. Duda, Peter E. Hart, David G. Stork (2001) Pattern classification (2nd edition), Wiley, New York, ISBN 0-471-05669-3.
 * Christopher Bishop (1995). Neural Networks for Pattern Recognition, Oxford University Press. ISBN 0-19-853864-2.
 * Stuart Russell & Peter Norvig, (2009). Artificial Intelligence – A Modern Approach Archived 2011-02-28 at the Wayback Machine. Pearson, ISBN 9789332543515.
 * Ray Solomonoff, An Inductive Inference Machine, IRE Convention Record, Section on Information Theory, Part 2, pp., 56–62, 1957.
 * Ray Solomonoff, An Inductive Inference Machine Archived 2011-04-26 at the Wayback Machine A privately circulated report from the 1956 Dartmouth Summer Research Conference on AI.
 * Kevin P. Murphy (2021). Probabilistic Machine Learning: An Introduction Archived 2021-04-11 at the Wayback Machine, MIT Press.

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Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. [1]  It is seen as a part of artificial intelligence. 
 Machine learning algorithms build a model based on sample data, known as training data, in order to make predictions or decisions without being explicitly programmed to do so. [2]  Machine learning algorithms are used in a wide variety of applications, such as in medicine, email filtering, speech recognition, agriculture, and computer vision, where it is difficult or unfeasible to develop conventional algorithms to perform the needed tasks. [3]   [4] 
 A subset of machine learning is closely related to computational statistics, which focuses on making predictions using computers, but not all machine learning is statistical learning. The study of mathematical optimization delivers methods, theory and application domains to the field of machine learning. Data mining is a related field of study, focusing on exploratory data analysis through unsupervised learning. [6]   [7]  
 Some implementations of machine learning use data and neural networks in a way that mimics the working of a biological brain. [8]   [9]  
 In its application across business problems, machine learning is also referred to as predictive analytics.
Overview[edit]
Learning algorithms work on the basis that strategies, algorithms, and inferences that worked well in the past are likely to continue working well in the future. These inferences can be obvious, such as "since the sun rose every morning for the last 10,000 days, it will probably rise tomorrow morning as well". They can be nuanced, such as "X% of families have geographically separate species with color variants, so there is a Y% chance that undiscovered black swans exist". [10] 
 Machine learning programs can perform tasks without being explicitly programmed to do so. It involves computers learning from data provided so that they carry out certain tasks. For simple tasks assigned to computers, it is possible to program algorithms telling the machine how to execute all steps required to solve the problem at hand; on the computer's part, no learning is needed. For more advanced tasks, it can be challenging for a human to manually create the needed algorithms. In practice, it can turn out to be more effective to help the machine develop its own algorithm, rather than having human programmers specify every needed step. [11] 
 The discipline of machine learning employs various approaches to teach computers to accomplish tasks where no fully satisfactory algorithm is available. In cases where vast numbers of potential answers exist, one approach is to label some of the correct answers as valid. This can then be used as training data for the computer to improve the algorithm(s) it uses to determine correct answers. For example, to train a system for the task of digital character recognition, the MNIST dataset of handwritten digits has often been used. [11] 
History and relationships to other fields[edit]
The term machine learning was coined in 1959 by Arthur Samuel, an IBM employee and pioneer in the field of computer gaming and artificial intelligence. [12]   [13]  The synonym self-teaching computers was also used in this time period. [14]   [15] 
 By the early 1960s an experimental "learning machine" with punched tape memory, called CyberTron, had been developed by Raytheon Company to analyze sonar signals, electrocardiograms, and speech patterns using rudimentary reinforcement learning. It was repetitively "trained" by a human operator/teacher to recognize patterns and equipped with a "goof" button to cause it to re-evaluate incorrect decisions. [16]  A representative book on research into machine learning during the 1960s was Nilsson's book on Learning Machines, dealing mostly with machine learning for pattern classification. [17]  Interest related to pattern recognition continued into the 1970s, as described by Duda and Hart in 1973. [18]  In 1981 a report was given on using teaching strategies so that a neural network learns to recognize 40 characters (26 letters, 10 digits, and 4 special symbols) from a computer terminal. [19] 
  Tom M. Mitchell provided a widely quoted, more formal definition of the algorithms studied in the machine learning field: "A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured by P, improves with experience E." [20]  This definition of the tasks in which machine learning is concerned offers a fundamentally operational definition rather than defining the field in cognitive terms. This follows Alan Turing's proposal in his paper "Computing Machinery and Intelligence", in which the question "Can machines think?" is replaced with the question "Can machines do what we (as thinking entities) can do?". [21] 
 Modern-day machine learning has two objectives, one is to classify data based on models which have been developed, the other purpose is to make predictions for future outcomes based on these models. A hypothetical algorithm specific to classifying data may use computer vision of moles coupled with supervised learning in order to train it to classify the cancerous moles. A machine learning algorithm for stock trading may inform the trader of future potential predictions. [22] 
Artificial intelligence[edit]
      Machine learning as subfield of AI [23]    
      Part of machine learning as subfield of AI or part of AI as subfield of machine learning [24]    
As a scientific endeavor, machine learning grew out of the quest for artificial intelligence. In the early days of AI as an academic discipline, some researchers were interested in having machines learn from data. They attempted to approach the problem with various symbolic methods, as well as what was then termed "neural networks"; these were mostly perceptrons and other models that were later found to be reinventions of the generalized linear models of statistics. [25]  Probabilistic reasoning was also employed, especially in automated medical diagnosis. [26]  : 488 
 However, an increasing emphasis on the logical, knowledge-based approach caused a rift between AI and machine learning. Probabilistic systems were plagued by theoretical and practical problems of data acquisition and representation. [26]  : 488  By 1980, expert systems had come to dominate AI, and statistics was out of favor. [27]  Work on symbolic/knowledge-based learning did continue within AI, leading to inductive logic programming, but the more statistical line of research was now outside the field of AI proper, in pattern recognition and information retrieval. [26]  : 708–710, 755  Neural networks research had been abandoned by AI and computer science around the same time. This line, too, was continued outside the AI/CS field, as "connectionism", by researchers from other disciplines including Hopfield, Rumelhart, and Hinton. Their main success came in the mid-1980s with the reinvention of backpropagation. [26]  : 25 
 Machine learning (ML), reorganized as a separate field, started to flourish in the 1990s. The field changed its goal from achieving artificial intelligence to tackling solvable problems of a practical nature. It shifted focus away from the symbolic approaches it had inherited from AI, and toward methods and models borrowed from statistics, fuzzy logic, and probability theory. [27] 
 The difference between ML and AI is frequently misunderstood. ML learns and predicts based on passive observations, whereas AI implies an agent interacting with the environment to learn and take actions that maximize its chance of successfully achieving its goals. [28] 
 As of 2020, many sources continue to assert that ML remains a subfield of AI. [29]   [30]   [27]  Others have the view that not all ML is part of AI, but only an 'intelligent subset' of ML should be considered AI. [5]   [31]   [32] 
Data mining[edit]
Machine learning and data mining often employ the same methods and overlap significantly, but while machine learning focuses on prediction, based on known properties learned from the training data, data mining focuses on the discovery of (previously) unknown properties in the data (this is the analysis step of knowledge discovery in databases). Data mining uses many machine learning methods, but with different goals; on the other hand, machine learning also employs data mining methods as "unsupervised learning" or as a preprocessing step to improve learner accuracy. Much of the confusion between these two research communities (which do often have separate conferences and separate journals, ECML PKDD being a major exception) comes from the basic assumptions they work with: in machine learning, performance is usually evaluated with respect to the ability to reproduce known knowledge, while in knowledge discovery and data mining (KDD) the key task is the discovery of previously unknown knowledge. Evaluated with respect to known knowledge, an uninformed (unsupervised) method will easily be outperformed by other supervised methods, while in a typical KDD task, supervised methods cannot be used due to the unavailability of training data.
Optimization[edit]
Machine learning also has intimate ties to optimization: many learning problems are formulated as minimization of some loss function on a training set of examples. Loss functions express the discrepancy between the predictions of the model being trained and the actual problem instances (for example, in classification, one wants to assign a label to instances, and models are trained to correctly predict the pre-assigned labels of a set of examples). [33] 
Generalization[edit]
The difference between optimization and machine learning arises from the goal of generalization: while optimization algorithms can minimize the loss on a training set, machine learning is concerned with minimizing the loss on unseen samples. Characterizing the generalization of various learning algorithms is an active topic of current research, especially for deep learning algorithms.
Statistics[edit]
Machine learning and statistics are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population inferences from a sample, while machine learning finds generalizable predictive patterns. [34]  According to Michael I. Jordan, the ideas of machine learning, from methodological principles to theoretical tools, have had a long pre-history in statistics. [35]  He also suggested the term data science as a placeholder to call the overall field. [35] 
  Leo Breiman distinguished two statistical modeling paradigms: data model and algorithmic model, [29]  wherein "algorithmic model" means more or less the machine learning algorithms like Random Forest.
 Some statisticians have adopted methods from machine learning, leading to a combined field that they call statistical learning. [30] 
Physics[edit]
Analytical and computational techniques derived from statistical physics of disordered systems, can be extended to large-scale problems, including machine learning, e.g., to analyze the weight space of deep neural networks. [36]  Statistical physics is thus finding applications in the area of medical diagnostics. [37] 
 Theory[edit]
A core objective of a learner is to generalize from its experience. [5]   [31]  Generalization in this context is the ability of a learning machine to perform accurately on new, unseen examples/tasks after having experienced a learning data set. The training examples come from some generally unknown probability distribution (considered representative of the space of occurrences) and the learner has to build a general model about this space that enables it to produce sufficiently accurate predictions in new cases.
 The computational analysis of machine learning algorithms and their performance is a branch of theoretical computer science known as computational learning theory via the Probably Approximately Correct Learning (PAC) model. Because training sets are finite and the future is uncertain, learning theory usually does not yield guarantees of the performance of algorithms. Instead, probabilistic bounds on the performance are quite common. The bias–variance decomposition is one way to quantify generalization error.
 For the best performance in the context of generalization, the complexity of the hypothesis should match the complexity of the function underlying the data. If the hypothesis is less complex than the function, then the model has under fitted the data. If the complexity of the model is increased in response, then the training error decreases. But if the hypothesis is too complex, then the model is subject to overfitting and generalization will be poorer. [32] 
 In addition to performance bounds, learning theorists study the time complexity and feasibility of learning. In computational learning theory, a computation is considered feasible if it can be done in polynomial time. There are two kinds of time complexity results: Positive results show that a certain class of functions can be learned in polynomial time. Negative results show that certain classes cannot be learned in polynomial time.
Approaches[edit]
Machine learning approaches are traditionally divided into three broad categories, which correspond to learning paradigms, depending on the nature of the "signal" or "feedback" available to the learning system:
  Supervised learning: The computer is presented with example inputs and their desired outputs, given by a "teacher", and the goal is to learn a general rule that maps inputs to outputs.
 Unsupervised learning: No labels are given to the learning algorithm, leaving it on its own to find structure in its input. Unsupervised learning can be a goal in itself (discovering hidden patterns in data) or a means towards an end (feature learning).
 Reinforcement learning: A computer program interacts with a dynamic environment in which it must perform a certain goal (such as driving a vehicle or playing a game against an opponent). As it navigates its problem space, the program is provided feedback that's analogous to rewards, which it tries to maximize. [5]   
Supervised learning[edit]
      A support-vector machine is a supervised learning model that divides the data into regions separated by a linear boundary. Here, the linear boundary divides the black circles from the white.  
Supervised learning algorithms build a mathematical model of a set of data that contains both the inputs and the desired outputs. [38]  The data is known as training data, and consists of a set of training examples. Each training example has one or more inputs and the desired output, also known as a supervisory signal. In the mathematical model, each training example is represented by an array or vector, sometimes called a feature vector, and the training data is represented by a matrix. Through iterative optimization of an objective function, supervised learning algorithms learn a function that can be used to predict the output associated with new inputs. [39]  An optimal function will allow the algorithm to correctly determine the output for inputs that were not a part of the training data. An algorithm that improves the accuracy of its outputs or predictions over time is said to have learned to perform that task. [20] 
 Types of supervised-learning algorithms include active learning, classification and regression. [28]  Classification algorithms are used when the outputs are restricted to a limited set of values, and regression algorithms are used when the outputs may have any numerical value within a range. As an example, for a classification algorithm that filters emails, the input would be an incoming email, and the output would be the name of the folder in which to file the email.
  Similarity learning is an area of supervised machine learning closely related to regression and classification, but the goal is to learn from examples using a similarity function that measures how similar or related two objects are. It has applications in ranking, recommendation systems, visual identity tracking, face verification, and speaker verification.
Unsupervised learning[edit]
Unsupervised learning algorithms take a set of data that contains only inputs, and find structure in the data, like grouping or clustering of data points. The algorithms, therefore, learn from test data that has not been labeled, classified or categorized. Instead of responding to feedback, unsupervised learning algorithms identify commonalities in the data and react based on the presence or absence of such commonalities in each new piece of data. A central application of unsupervised learning is in the field of density estimation in statistics, such as finding the probability density function. [40]  Though unsupervised learning encompasses other domains involving summarizing and explaining data features.
 Cluster analysis is the assignment of a set of observations into subsets (called clusters) so that observations within the same cluster are similar according to one or more predesignated criteria, while observations drawn from different clusters are dissimilar. Different clustering techniques make different assumptions on the structure of the data, often defined by some similarity metric and evaluated, for example, by internal compactness, or the similarity between members of the same cluster, and separation, the difference between clusters. Other methods are based on estimated density and graph connectivity.
Semi-supervised learning[edit]
Semi-supervised learning falls between unsupervised learning (without any labeled training data) and supervised learning (with completely labeled training data). Some of the training examples are missing training labels, yet many machine-learning researchers have found that unlabeled data, when used in conjunction with a small amount of labeled data, can produce a considerable improvement in learning accuracy.
 In weakly supervised learning, the training labels are noisy, limited, or imprecise; however, these labels are often cheaper to obtain, resulting in larger effective training sets. [41] 
Reinforcement learning[edit]
Reinforcement learning is an area of machine learning concerned with how software agents ought to take actions in an environment so as to maximize some notion of cumulative reward. Due to its generality, the field is studied in many other disciplines, such as game theory, control theory, operations research, information theory, simulation-based optimization, multi-agent systems, swarm intelligence, statistics and genetic algorithms. In machine learning, the environment is typically represented as a Markov decision process (MDP). Many reinforcements learning algorithms use dynamic programming techniques. [42]  Reinforcement learning algorithms do not assume knowledge of an exact mathematical model of the MDP and are used when exact models are infeasible. Reinforcement learning algorithms are used in autonomous vehicles or in learning to play a game against a human opponent.
Dimensionality reduction[edit]
Dimensionality reduction is a process of reducing the number of random variables under consideration by obtaining a set of principal variables. [43]  In other words, it is a process of reducing the dimension of the feature set, also called the "number of features". Most of the dimensionality reduction techniques can be considered as either feature elimination or extraction. One of the popular methods of dimensionality reduction is principal component analysis (PCA). PCA involves changing higher-dimensional data (e.g., 3D) to a smaller space (e.g., 2D). This results in a smaller dimension of data (2D instead of 3D), while keeping all original variables in the model without changing the data. [44] 
The manifold hypothesis proposes that high-dimensional data sets lie along low-dimensional manifolds, and many dimensionality reduction techniques make this assumption, leading to the area of manifold learning and manifold regularization.
Other types[edit]
Other approaches have been developed which don't fit neatly into this three-fold categorization, and sometimes more than one is used by the same machine learning system. For example, topic modeling, meta-learning. [45] 
 As of 2022, deep learning is the dominant approach for much ongoing work in the field of machine learning. [11] 
Self-learning[edit]
Self-learning, as a machine learning paradigm was introduced in 1982 along with a neural network capable of self-learning, named crossbar adaptive array (CAA). [46]  It is learning with no external rewards and no external teacher advice. The CAA self-learning algorithm computes, in a crossbar fashion, both decisions about actions and emotions (feelings) about consequence situations. The system is driven by the interaction between cognition and emotion. [47] 
The self-learning algorithm updates a memory matrix W =||w(a,s)|| such that in each iteration executes the following machine learning routine: 
 in situation s perform action a 
receive consequence situation s' 
compute emotion of being in consequence situation v(s') 
update crossbar memory w'(a,s) = w(a,s) + v(s')  
It is a system with only one input, situation, and only one output, action (or behavior) a. There is neither a separate reinforcement input nor an advice input from the environment. The backpropagated value (secondary reinforcement) is the emotion toward the consequence situation. The CAA exists in two environments, one is the behavioral environment where it behaves, and the other is the genetic environment, wherefrom it initially and only once receives initial emotions about situations to be encountered in the behavioral environment. After receiving the genome (species) vector from the genetic environment, the CAA learns a goal-seeking behavior, in an environment that contains both desirable and undesirable situations. [48] 
Feature learning[edit]
Several learning algorithms aim at discovering better representations of the inputs provided during training. [49]  Classic examples include principal component analysis and cluster analysis. Feature learning algorithms, also called representation learning algorithms, often attempt to preserve the information in their input but also transform it in a way that makes it useful, often as a pre-processing step before performing classification or predictions. This technique allows reconstruction of the inputs coming from the unknown data-generating distribution, while not being necessarily faithful to configurations that are implausible under that distribution. This replaces manual feature engineering, and allows a machine to both learn the features and use them to perform a specific task.
 Feature learning can be either supervised or unsupervised. In supervised feature learning, features are learned using labeled input data. Examples include artificial neural networks, multilayer perceptrons, and supervised dictionary learning. In unsupervised feature learning, features are learned with unlabeled input data. Examples include dictionary learning, independent component analysis, autoencoders, matrix factorization  [50]  and various forms of clustering. [51]   [52]   [53] 
  Manifold learning algorithms attempt to do so under the constraint that the learned representation is low-dimensional. Sparse coding algorithms attempt to do so under the constraint that the learned representation is sparse, meaning that the mathematical model has many zeros. Multilinear subspace learning algorithms aim to learn low-dimensional representations directly from tensor representations for multidimensional data, without reshaping them into higher-dimensional vectors. [54]  Deep learning algorithms discover multiple levels of representation, or a hierarchy of features, with higher-level, more abstract features defined in terms of (or generating) lower-level features. It has been argued that an intelligent machine is one that learns a representation that disentangles the underlying factors of variation that explain the observed data. [55] 
 Feature learning is motivated by the fact that machine learning tasks such as classification often require input that is mathematically and computationally convenient to process. However, real-world data such as images, video, and sensory data has not yielded attempts to algorithmically define specific features. An alternative is to discover such features or representations through examination, without relying on explicit algorithms.
Sparse dictionary learning[edit]
Sparse dictionary learning is a feature learning method where a training example is represented as a linear combination of basis functions, and is assumed to be a sparse matrix. The method is strongly NP-hard and difficult to solve approximately. [56]  A popular heuristic method for sparse dictionary learning is the K-SVD algorithm. Sparse dictionary learning has been applied in several contexts. In classification, the problem is to determine the class to which a previously unseen training example belongs. For a dictionary where each class has already been built, a new training example is associated with the class that is best sparsely represented by the corresponding dictionary. Sparse dictionary learning has also been applied in image de-noising. The key idea is that a clean image patch can be sparsely represented by an image dictionary, but the noise cannot. [57] 
Anomaly detection[edit]
In data mining, anomaly detection, also known as outlier detection, is the identification of rare items, events or observations which raise suspicions by differing significantly from the majority of the data. [58]  Typically, the anomalous items represent an issue such as bank fraud, a structural defect, medical problems or errors in a text. Anomalies are referred to as outliers, novelties, noise, deviations and exceptions. [59] 
 In particular, in the context of abuse and network intrusion detection, the interesting objects are often not rare objects, but unexpected bursts of inactivity. This pattern does not adhere to the common statistical definition of an outlier as a rare object. Many outlier detection methods (in particular, unsupervised algorithms) will fail on such data unless aggregated appropriately. Instead, a cluster analysis algorithm may be able to detect the micro-clusters formed by these patterns. [60] 
 Three broad categories of anomaly detection techniques exist. [61]  Unsupervised anomaly detection techniques detect anomalies in an unlabeled test data set under the assumption that the majority of the instances in the data set are normal, by looking for instances that seem to fit the least to the remainder of the data set. Supervised anomaly detection techniques require a data set that has been labeled as "normal" and "abnormal" and involves training a classifier (the key difference to many other statistical classification problems is the inherently unbalanced nature of outlier detection). Semi-supervised anomaly detection techniques construct a model representing normal behavior from a given normal training data set and then test the likelihood of a test instance to be generated by the model.
Robot learning[edit]
 Robot learning is inspired by a multitude of machine learning methods, starting from supervised learning, reinforcement learning, [62]   [63]  and finally meta-learning (e.g. MAML).
Association rules[edit]
Association rule learning is a rule-based machine learning method for discovering relationships between variables in large databases. It is intended to identify strong rules discovered in databases using some measure of "interestingness". [64] 
 Rule-based machine learning is a general term for any machine learning method that identifies, learns, or evolves "rules" to store, manipulate or apply knowledge. The defining characteristic of a rule-based machine learning algorithm is the identification and utilization of a set of relational rules that collectively represent the knowledge captured by the system. This is in contrast to other machine learning algorithms that commonly identify a singular model that can be universally applied to any instance in order to make a prediction. [65]  Rule-based machine learning approaches include learning classifier systems, association rule learning, and artificial immune systems.
 Based on the concept of strong rules, Rakesh Agrawal, Tomasz Imieliński and Arun Swami introduced association rules for discovering regularities between products in large-scale transaction data recorded by point-of-sale (POS) systems in supermarkets. [66]  For example, the rule found in the sales data of a supermarket would indicate that if a customer buys onions and potatoes together, they are likely to also buy hamburger meat. Such information can be used as the basis for decisions about marketing activities such as promotional pricing or product placements. In addition to market basket analysis, association rules are employed today in application areas including Web usage mining, intrusion detection, continuous production, and bioinformatics. In contrast with sequence mining, association rule learning typically does not consider the order of items either within a transaction or across transactions.
 Learning classifier systems (LCS) are a family of rule-based machine learning algorithms that combine a discovery component, typically a genetic algorithm, with a learning component, performing either supervised learning, reinforcement learning, or unsupervised learning. They seek to identify a set of context-dependent rules that collectively store and apply knowledge in a piecewise manner in order to make predictions. [67] 
 Inductive logic programming (ILP) is an approach to rule learning using logic programming as a uniform representation for input examples, background knowledge, and hypotheses. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesized logic program that entails all positive and no negative examples. Inductive programming is a related field that considers any kind of programming language for representing hypotheses (and not only logic programming), such as functional programs.
 Inductive logic programming is particularly useful in bioinformatics and natural language processing. Gordon Plotkin and Ehud Shapiro laid the initial theoretical foundation for inductive machine learning in a logical setting. [68]   [69]   [70]  Shapiro built their first implementation (Model Inference System) in 1981: a Prolog program that inductively inferred logic programs from positive and negative examples. [71]  The term inductive here refers to philosophical induction, suggesting a theory to explain observed facts, rather than mathematical induction, proving a property for all members of a well-ordered set.
Models[edit]
Performing machine learning involves creating a model, which is trained on some training data and then can process additional data to make predictions. Various types of models have been used and researched for machine learning systems.
Artificial neural networks[edit]
      An artificial neural network is an interconnected group of nodes, akin to the vast network of neurons in a brain. Here, each circular node represents an artificial neuron and an arrow represents a connection from the output of one artificial neuron to the input of another.  
Artificial neural networks (ANNs), or connectionist systems, are computing systems vaguely inspired by the biological neural networks that constitute animal brains. Such systems "learn" to perform tasks by considering examples, generally without being programmed with any task-specific rules.
 An ANN is a model based on a collection of connected units or nodes called "artificial neurons", which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit information, a "signal", from one artificial neuron to another. An artificial neuron that receives a signal can process it and then signal additional artificial neurons connected to it. In common ANN implementations, the signal at a connection between artificial neurons is a real number, and the output of each artificial neuron is computed by some non-linear function of the sum of its inputs. The connections between artificial neurons are called "edges". Artificial neurons and edges typically have a weight that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Artificial neurons may have a threshold such that the signal is only sent if the aggregate signal crosses that threshold. Typically, artificial neurons are aggregated into layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first layer (the input layer) to the last layer (the output layer), possibly after traversing the layers multiple times.
 The original goal of the ANN approach was to solve problems in the same way that a human brain would. However, over time, attention moved to performing specific tasks, leading to deviations from biology. Artificial neural networks have been used on a variety of tasks, including computer vision, speech recognition, machine translation, social network filtering, playing board and video games and medical diagnosis.
  Deep learning consists of multiple hidden layers in an artificial neural network. This approach tries to model the way the human brain processes light and sound into vision and hearing. Some successful applications of deep learning are computer vision and speech recognition. [72] 
Decision trees[edit]
      A decision tree showing survival probability of passengers on the Titanic   
Decision tree learning uses a decision tree as a predictive model to go from observations about an item (represented in the branches) to conclusions about the item's target value (represented in the leaves). It is one of the predictive modeling approaches used in statistics, data mining, and machine learning. Tree models where the target variable can take a discrete set of values are called classification trees; in these tree structures, leaves represent class labels, and branches represent conjunctions of features that lead to those class labels. Decision trees where the target variable can take continuous values (typically real numbers) are called regression trees. In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making. In data mining, a decision tree describes data, but the resulting classification tree can be an input for decision-making.
Support-vector machines[edit]
Support-vector machines (SVMs), also known as support-vector networks, are a set of related supervised learning methods used for classification and regression. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that predicts whether a new example falls into one category. [73]  An SVM training algorithm is a non-probabilistic, binary, linear classifier, although methods such as Platt scaling exist to use SVM in a probabilistic classification setting. In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces.
Regression analysis[edit]
      Illustration of linear regression on a data set  
Regression analysis encompasses a large variety of statistical methods to estimate the relationship between input variables and their associated features. Its most common form is linear regression, where a single line is drawn to best fit the given data according to a mathematical criterion such as ordinary least squares. The latter is often extended by regularization methods to mitigate overfitting and bias, as in ridge regression. When dealing with non-linear problems, go-to models include polynomial regression (for example, used for trendline fitting in Microsoft Excel [74] ), logistic regression (often used in statistical classification) or even kernel regression, which introduces non-linearity by taking advantage of the kernel trick to implicitly map input variables to higher-dimensional space.
Bayesian networks[edit]
      A simple Bayesian network. Rain influences whether the sprinkler is activated, and both rain and the sprinkler influence whether the grass is wet.  
A Bayesian network, belief network, or directed acyclic graphical model is a probabilistic graphical model that represents a set of random variables and their conditional independence with a directed acyclic graph (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms exist that perform inference and learning. Bayesian networks that model sequences of variables, like speech signals or protein sequences, are called dynamic Bayesian networks. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty are called influence diagrams.
Gaussian processes[edit]
      An example of Gaussian Process Regression (prediction) compared with other regression models [75]    
A Gaussian process is a stochastic process in which every finite collection of the random variables in the process has a multivariate normal distribution, and it relies on a pre-defined covariance function, or kernel, that models how pairs of points relate to each other depending on their locations.
 Given a set of observed points, or input–output examples, the distribution of the (unobserved) output of a new point as function of its input data, can be directly computed by looking like the observed points and the covariances between those points and the new, unobserved point.
 Gaussian processes are popular surrogate models in Bayesian optimization used to do hyperparameter optimization.
Genetic algorithms[edit]
A genetic algorithm (GA) is a search algorithm and heuristic technique that mimics the process of natural selection, using methods such as mutation and crossover to generate new genotypes in the hope of finding good solutions to a given problem. In machine learning, genetic algorithms were used in the 1980s and 1990s. [76]   [77]  Conversely, machine learning techniques have been used to improve the performance of genetic and evolutionary algorithms. [78] 
Training models[edit]
Typically, machine learning models require a high quantity of reliable data in order for the models to perform accurate predictions. When training a machine learning model, machine learning engineers need to target and collect a large and representative sample of data. Data from the training set can be as varied as a corpus of text, a collection of images, sensor data, and data collected from individual users of a service. Overfitting is something to watch out for when training a machine learning model. Trained models derived from biased or non-evaluated data can result in skewed or undesired predictions. Bias models may result in detrimental outcomes thereby furthering the negative impacts on society or objectives. Algorithmic bias is a potential result of data not being fully prepared for training. Machine learning ethics is becoming a field of study and notably be integrated within machine learning engineering teams.
Federated learning[edit]
Federated learning is an adapted form of distributed artificial intelligence to training machine learning models that decentralizes the training process, allowing for users' privacy to be maintained by not needing to send their data to a centralized server. This also increases efficiency by decentralizing the training process to many devices. For example, Gboard uses federated machine learning to train search query prediction models on users' mobile phones without having to send individual searches back to Google. [79] 
Applications[edit]
There are many applications for machine learning, including:
  Agriculture 
 Anatomy 
 Adaptive website 
 Affective computing 
 Astronomy 
 Automated decision-making 
 Banking 
 Behaviorism 
 Bioinformatics 
 Brain–machine interfaces 
 Cheminformatics 
 Citizen Science 
 Climate Science 
 Computer networks 
 Computer vision 
 Credit-card fraud detection
 Data quality 
 DNA sequence classification
 Economics 
 Financial market analysis [80]  
 General game playing 
 Handwriting recognition 
 Information retrieval 
 Insurance 
 Internet fraud detection
 Knowledge graph embedding 
 Linguistics 
 Machine learning control 
 Machine perception 
 Machine translation 
 Marketing 
 Medical diagnosis 
 Natural language processing 
 Natural language understanding 
 Online advertising 
 Optimization 
 Recommender systems 
 Robot locomotion 
 Search engines 
 Sentiment analysis 
 Sequence mining 
 Software engineering 
 Speech recognition 
 Structural health monitoring 
 Syntactic pattern recognition 
 Telecommunication 
 Theorem proving 
 Time-series forecasting 
 User behavior analytics  
In 2006, the media-services provider Netflix held the first "Netflix Prize" competition to find a program to better predict user preferences and improve the accuracy of its existing Cinematch movie recommendation algorithm by at least 10%. A joint team made up of researchers from AT&amp;T Labs-Research in collaboration with the teams Big Chaos and Pragmatic Theory built an ensemble model to win the Grand Prize in 2009 for $1 million. [81]  Shortly after the prize was awarded, Netflix realized that viewers' ratings were not the best indicators of their viewing patterns ("everything is a recommendation") and they changed their recommendation engine accordingly. [82]  In 2010 The Wall Street Journal wrote about the firm Rebellion Research and their use of machine learning to predict the financial crisis. [83]  In 2012, co-founder of Sun Microsystems, Vinod Khosla, predicted that 80% of medical doctors jobs would be lost in the next two decades to automated machine learning medical diagnostic software. [84]  In 2014, it was reported that a machine learning algorithm had been applied in the field of art history to study fine art paintings and that it may have revealed previously unrecognized influences among artists. [85]  In 2019 Springer Nature published the first research book created using machine learning. [86]  In 2020, machine learning technology was used to help make diagnoses and aid researchers in developing a cure for COVID-19. [87]  Machine learning was recently applied to predict the pro-environmental behavior of travelers. [88]  Recently, machine learning technology was also applied to optimize smartphone's performance and thermal behavior based on the user's interaction with the phone. [89]   [90]   [91] 
Limitations[edit]
Although machine learning has been transformative in some fields, machine-learning programs often fail to deliver expected results. [92]   [93]   [94]  Reasons for this are numerous: lack of (suitable) data, lack of access to the data, data bias, privacy problems, badly chosen tasks and algorithms, wrong tools and people, lack of resources, and evaluation problems. [95] 
 In 2018, a self-driving car from Uber failed to detect a pedestrian, who was killed after a collision. [96]  Attempts to use machine learning in healthcare with the IBM Watson system failed to deliver even after years of time and billions of dollars invested. [97]   [98] 
 Machine learning has been used as a strategy to update the evidence related to a systematic review and increased reviewer burden related to the growth of biomedical literature. While it has improved with training sets, it has not yet developed sufficiently to reduce the workload burden without limiting the necessary sensitivity for the findings research themselves. [99] 
Bias[edit]
Machine learning approaches in particular can suffer from different data biases. A machine learning system trained specifically on current customers may not be able to predict the needs of new customer groups that are not represented in the training data. When trained on man-made data, machine learning is likely to pick up the constitutional and unconscious biases already present in society. [100]  Language models learned from data have been shown to contain human-like biases. [101]   [102]  Machine learning systems used for criminal risk assessment have been found to be biased against black people. [103]   [104]  In 2015, Google photos would often tag black people as gorillas, [105]  and in 2018 this still was not well resolved, but Google reportedly was still using the workaround to remove all gorillas from the training data, and thus was not able to recognize real gorillas at all. [106]  Similar issues with recognizing non-white people have been found in many other systems. [107]  In 2016, Microsoft tested a chatbot that learned from Twitter, and it quickly picked up racist and sexist language. [108]  Because of such challenges, the effective use of machine learning may take longer to be adopted in other domains. [109]  Concern for fairness in machine learning, that is, reducing bias in machine learning and propelling its use for human good is increasingly expressed by artificial intelligence scientists, including Fei-Fei Li, who reminds engineers that "There's nothing artificial about AI...It's inspired by people, it's created by people, and—most importantly—it impacts people. It is a powerful tool we are only just beginning to understand, and that is a profound responsibility." [110] 
Explainability[edit]
Explainable AI (XAI), or Interpretable AI, or Explainable Machine Learning (XML), is artificial intelligence (AI) in which humans can understand the decisions or predictions made by the AI. It contrasts with the "black box" concept in machine learning where even its designers cannot explain why an AI arrived at a specific decision. By refining the mental models of users of AI-powered systems and dismantling their misconceptions, XAI promises to help users perform more effectively. XAI may be an implementation of the social right to explanation.
Overfitting[edit]
      The blue line could be an example of overfitting a linear function due to random noise.  
Settling on a bad, overly complex theory gerrymandered to fit all the past training data is known as overfitting. Many systems attempt to reduce overfitting by rewarding a theory in accordance with how well it fits the data but penalizing the theory in accordance with how complex the theory is. [10] 
Other limitations and vulnerabilities[edit]
Learners can also disappoint by "learning the wrong lesson". A toy example is that an image classifier trained only on pictures of brown horses and black cats might conclude that all brown patches are likely to be horses. [111]  A real-world example is that, unlike humans, current image classifiers often don't primarily make judgments from the spatial relationship between components of the picture, and they learn relationships between pixels that humans are oblivious to, but that still correlate with images of certain types of real objects. Modifying these patterns on a legitimate image can result in "adversarial" images that the system misclassifies. [112]   [113] 
 Adversarial vulnerabilities can also result in nonlinear systems, or from non-pattern perturbations. Some systems are so brittle that changing a single adversarial pixel predictably induces misclassification.[ citation needed ] Machine learning models are often vulnerable to manipulation and/or evasion via adversarial machine learning. [114] 
 Researchers have demonstrated how backdoors can be placed undetectably into classifying (e.g., for categories "spam" and well-visible "not spam" of posts) machine learning models which are often developed and/or trained by third parties. Parties can change the classification of any input, including in cases for which a type of data/software transparency is provided, possibly including white-box access. [115]   [116]   [117] 
Model assessments[edit]
Classification of machine learning models can be validated by accuracy estimation techniques like the holdout method, which splits the data in a training and test set (conventionally 2/3 training set and 1/3 test set designation) and evaluates the performance of the training model on the test set. In comparison, the K-fold-cross-validation method randomly partitions the data into K subsets and then K experiments are performed each respectively considering 1 subset for evaluation and the remaining K-1 subsets for training the model. In addition to the holdout and cross-validation methods, bootstrap, which samples n instances with replacement from the dataset, can be used to assess model accuracy. [118] 
 In addition to overall accuracy, investigators frequently report sensitivity and specificity meaning True Positive Rate (TPR) and True Negative Rate (TNR) respectively. Similarly, investigators sometimes report the false positive rate (FPR) as well as the false negative rate (FNR). However, these rates are ratios that fail to reveal their numerators and denominators. The total operating characteristic (TOC) is an effective method to express a model's diagnostic ability. TOC shows the numerators and denominators of the previously mentioned rates, thus TOC provides more information than the commonly used receiver operating characteristic (ROC) and ROC's associated area under the curve (AUC). [119] 
Ethics[edit]
Machine learning poses a host of ethical questions. Systems that are trained on datasets collected with biases may exhibit these biases upon use (algorithmic bias), thus digitizing cultural prejudices. [120]  For example, in 1988, the UK's Commission for Racial Equality found that St. George's Medical School had been using a computer program trained from data of previous admissions staff and this program had denied nearly 60 candidates who were found to be either women or had non-European sounding names. [100]  Using job hiring data from a firm with racist hiring policies may lead to a machine learning system duplicating the bias by scoring job applicants by similarity to previous successful applicants. [121]   [122]  Responsible collection of data and documentation of algorithmic rules used by a system thus is a critical part of machine learning.
 AI can be well-equipped to make decisions in technical fields, which rely heavily on data and historical information. These decisions rely on the objectivity and logical reasoning. [123]  Because human languages contain biases, machines trained on language  corpora  will necessarily also learn these biases. [124]   [125] 
 Other forms of ethical challenges, not related to personal biases, are seen in health care. There are concerns among health care professionals that these systems might not be designed in the public's interest but as income-generating machines. [126]  This is especially true in the United States where there is a long-standing ethical dilemma of improving health care, but also increase profits. For example, the algorithms could be designed to provide patients with unnecessary tests or medication in which the algorithm's proprietary owners hold stakes. There is potential for machine learning in health care to provide professionals an additional tool to diagnose, medicate, and plan recovery paths for patients, but this requires these biases to be mitigated. [127] 
Hardware[edit]
Since the 2010s, advances in both machine learning algorithms and computer hardware have led to more efficient methods for training deep neural networks (a particular narrow subdomain of machine learning) that contain many layers of non-linear hidden units. [128]  By 2019, graphic processing units (GPUs), often with AI-specific enhancements, had displaced CPUs as the dominant method of training large-scale commercial cloud AI. [129]  OpenAI estimated the hardware computing used in the largest deep learning projects from AlexNet (2012) to AlphaZero (2017), and found a 300,000-fold increase in the amount of compute required, with a doubling-time trendline of 3.4 months. [130]   [131] 
Neuromorphic/Physical Neural Networks[edit]
A physical neural network or Neuromorphic computer is a type of artificial neural network in which an electrically adjustable material is used to emulate the function of a neural synapse. "Physical" neural network is used to emphasize the reliance on physical hardware used to emulate neurons as opposed to software-based approaches. More generally the term is applicable to other artificial neural networks in which a memristor or other electrically adjustable resistance material is used to emulate a neural synapse. [132]   [133] 
Embedded Machine Learning[edit]
 Embedded Machine Learning is a sub-field of machine learning, where the machine learning model is run on embedded systems with limited computing resources such as wearable computers, edge devices and microcontrollers. [134]   [135]   [136]  Running machine learning model in embedded devices removes the need for transferring and storing data on cloud servers for further processing, henceforth, reducing data breaches and privacy leaks happening because of transferring data, and also minimizes theft of intellectual properties, personal data and business secrets. Embedded Machine Learning could be applied through several techniques including hardware acceleration, [137]   [138]  using approximate computing, [139]  optimization of machine learning models and many more. [140]   [141] 
Software[edit]
 Software suites containing a variety of machine learning algorithms include the following:
Free and open-source software[edit]
  Caffe 
 Deeplearning4j 
 DeepSpeed 
 ELKI 
 Google JAX 
 Infer.NET 
 Keras 
 Kubeflow 
 LightGBM 
 Mahout 
 Mallet 
 Microsoft Cognitive Toolkit 
 ML.NET 
 mlpack 
MLFlow
 MXNet 
 Neural Lab 
 OpenNN 
 Orange 
 pandas (software) 
 ROOT (TMVA with ROOT)
 scikit-learn 
 Shogun 
 Spark MLlib 
 SystemML 
 TensorFlow 
 Torch / PyTorch 
 Weka / MOA 
 XGBoost 
 Yooreeka  
Proprietary software with free and open-source editions[edit]
  KNIME 
 RapidMiner  
Proprietary software[edit]
  Amazon Machine Learning 
 Angoss KnowledgeSTUDIO
 Azure Machine Learning 
Ayasdi
 IBM Watson Studio 
 Google Cloud Vertex AI 
 Google Prediction API 
 IBM SPSS Modeler 
 KXEN Modeler 
 LIONsolver 
 Mathematica 
 MATLAB 
 Neural Designer 
 NeuroSolutions 
 Oracle Data Mining 
 Oracle AI Platform Cloud Service 
 PolyAnalyst 
 RCASE 
 SAS Enterprise Miner 
 SequenceL 
 Splunk 
 STATISTICA Data Miner 
Journals[edit]
  Journal of Machine Learning Research 
 Machine Learning 
 Nature Machine Intelligence 
 Neural Computation 
IEEE Transactions on Pattern Analysis and Machine Intelligence 
Conferences[edit]
  AAAI Conference on Artificial Intelligence 
 Association for Computational Linguistics (ACL) 
 European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD) 
 International Conference on Computational Intelligence Methods for Bioinformatics and Biostatistics (CIBB) 
 International Conference on Machine Learning (ICML) 
 International Conference on Learning Representations (ICLR) 
 International Conference on Intelligent Robots and Systems (IROS) 
 Conference on Knowledge Discovery and Data Mining (KDD) 
 Conference on Neural Information Processing Systems (NeurIPS)  
See also[edit]
  Automated machine learning – Process of automating the application of machine learning
 Big data – Information assets characterized by high volume, velocity, and variety
 Differentiable programming – Programming paradigm
 List of important publications in machine learning 
 List of datasets for machine-learning research  
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Sources[edit]
   Domingos, Pedro (September 22, 2015). The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World. Basic Books. ISBN  978-0465065707 . 
  Nilsson, Nils (1998).  Artificial Intelligence: A New Synthesis . Morgan Kaufmann. ISBN  978-1-55860-467-4 . Archived from the original on 26 July 2020. Retrieved 18 November 2019. 
  Russell, Stuart J.; Norvig, Peter (2003),  Artificial Intelligence: A Modern Approach  (2nd ed.), Upper Saddle River, New Jersey: Prentice Hall, ISBN  0-13-790395-2  .
 Poole, David; Mackworth, Alan; Goebel, Randy (1998).  Computational Intelligence: A Logical Approach . New York: Oxford University Press. ISBN  978-0-19-510270-3 . Archived from the original on 26 July 2020. Retrieved 22 August 2020.  
Further reading[edit]
 Nils J. Nilsson,  Introduction to Machine Learning Archived 2019-08-16 at the Wayback Machine .
 Trevor Hastie, Robert Tibshirani and Jerome H. Friedman (2001).  The Elements of Statistical Learning Archived 2013-10-27 at the Wayback Machine , Springer. ISBN 0-387-95284-5.
 Pedro Domingos (September 2015),  The Master Algorithm , Basic Books, ISBN 978-0-465-06570-7 
Ian H. Witten and Eibe Frank (2011). Data Mining: Practical machine learning tools and techniques Morgan Kaufmann, 664pp., ISBN 978-0-12-374856-0.
Ethem Alpaydin (2004). Introduction to Machine Learning, MIT Press, ISBN 978-0-262-01243-0.
 David J. C. MacKay.  Information Theory, Inference, and Learning Algorithms Archived 2016-02-17 at the Wayback Machine  Cambridge: Cambridge University Press, 2003. ISBN 0-521-64298-1 
 Richard O. Duda, Peter E. Hart, David G. Stork (2001) Pattern classification (2nd edition), Wiley, New York, ISBN 0-471-05669-3.
 Christopher Bishop (1995). Neural Networks for Pattern Recognition, Oxford University Press. ISBN 0-19-853864-2.
Stuart Russell &amp; Peter Norvig, (2009).  Artificial Intelligence – A Modern Approach Archived 2011-02-28 at the Wayback Machine . Pearson, ISBN 9789332543515.
 Ray Solomonoff, An Inductive Inference Machine, IRE Convention Record, Section on Information Theory, Part 2, pp., 56–62, 1957.
 Ray Solomonoff,  An Inductive Inference Machine Archived 2011-04-26 at the Wayback Machine  A privately circulated report from the 1956 Dartmouth Summer Research Conference on AI.
Kevin P. Murphy (2021).  Probabilistic Machine Learning: An Introduction Archived 2021-04-11 at the Wayback Machine , MIT Press. 
External links[edit]
    Quotations related to Machine learning at Wikiquote
 International Machine Learning Society 
 mloss is an academic database of open-source machine learning software.
Machine learning - Wikipedia
https://en.wikipedia.org/wiki/Machine_learning
https://en.wikipedia.org/wiki/Supervised_learning
Supervised learning - Wikipedia
2002-01-08
Authority control National libraries Israel United States
<div><div>
	<p>From Wikipedia, the free encyclopedia</p>
	</div><div>
<p><b>Supervised learning (SL)</b> is a <a href="/wiki/Machine_learning">machine learning</a> paradigm for problems where the available data consists of labelled examples, meaning that each data point contains features (covariates) and an associated label. The goal of supervised learning algorithms is learning a function that <a href="/wiki/Map_(mathematics)">maps</a> feature vectors (inputs) to labels (output), based on example input-output pairs.<sup><a href="#cite_note-1">[1]</a></sup> It infers a function from <i>labeled <a href="/wiki/Training_set">training data</a></i> consisting of a set of <i>training examples</i>.<sup><a href="#cite_note-2">[2]</a></sup> In supervised learning, each example is a <i>pair</i> consisting of an input object (typically a vector) and a desired output value (also called the <i>supervisory signal</i>). A supervised learning algorithm analyzes the training data and produces an inferred function, which can be used for mapping new examples. An optimal scenario will allow for the algorithm to correctly determine the class labels for unseen instances. This requires the learning algorithm to generalize from the training data to unseen situations in a "reasonable" way (see <a href="/wiki/Inductive_bias">inductive bias</a>). This statistical quality of an algorithm is measured through the so-called <a href="/wiki/Generalization_error">generalization error</a>.
</p>
<h2>Steps to follow[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=1">edit</a>]</h2>
<p>To solve a given problem of supervised learning, one has to perform the following steps:
</p>
<ol><li>Determine the type of training examples. Before doing anything else, the user should decide what kind of data is to be used as a training set. In the case of <a href="/wiki/Handwriting_analysis">handwriting analysis</a>, for example, this might be a single handwritten character, an entire handwritten word, an entire sentence of handwriting or perhaps a full paragraph of handwriting.</li>
<li>Gather a training set. The training set needs to be representative of the real-world use of the function. Thus, a set of input objects is gathered and corresponding outputs are also gathered, either from human experts or from measurements.</li>
<li>Determine the input feature representation of the learned function. The accuracy of the learned function depends strongly on how the input object is represented. Typically, the input object is transformed into a <a href="/wiki/Feature_vector">feature vector</a>, which contains a number of features that are descriptive of the object. The number of features should not be too large, because of the <a href="/wiki/Curse_of_dimensionality">curse of dimensionality</a>; but should contain enough information to accurately predict the output.</li>
<li>Determine the structure of the learned function and corresponding learning algorithm. For example, the engineer may choose to use <a href="/wiki/Support-vector_machine">support-vector machines</a> or <a href="/wiki/Decision_tree_learning">decision trees</a>.</li>
<li>Complete the design. Run the learning algorithm on the gathered training set. Some supervised learning algorithms require the user to determine certain control parameters. These parameters may be adjusted by optimizing performance on a subset (called a <i>validation</i> set) of the training set, or via <a href="/wiki/Cross-validation_(statistics)">cross-validation</a>.</li>
<li>Evaluate the accuracy of the learned function. After parameter adjustment and learning, the performance of the resulting function should be measured on a test set that is separate from the training set.</li></ol>
<h2>Algorithm choice[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=2">edit</a>]</h2>
<p>A wide range of supervised learning algorithms are available, each with its strengths and weaknesses. There is no single learning algorithm that works best on all supervised learning problems (see the <a href="/wiki/No_free_lunch_in_search_and_optimization">No free lunch theorem</a>).
</p><p>There are four major issues to consider in supervised learning:
</p>
<h3>Bias-variance tradeoff[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=3">edit</a>]</h3>
<p>A first issue is the tradeoff between <i>bias</i> and <i>variance</i>.<sup><a href="#cite_note-3">[3]</a></sup> Imagine that we have available several different, but equally good, training data sets. A learning algorithm is biased for a particular input if, when trained on each of these data sets, it is systematically incorrect when predicting the correct output for . A learning algorithm has high variance for a particular input if it predicts different output values when trained on different training sets. The prediction error of a learned classifier is related to the sum of the bias and the variance of the learning algorithm.<sup><a href="#cite_note-4">[4]</a></sup> Generally, there is a tradeoff between bias and variance. A learning algorithm with low bias must be "flexible" so that it can fit the data well. But if the learning algorithm is too flexible, it will fit each training data set differently, and hence have high variance. A key aspect of many supervised learning methods is that they are able to adjust this tradeoff between bias and variance (either automatically or by providing a bias/variance parameter that the user can adjust).
</p>
<h3>Function complexity and amount of training data[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=4">edit</a>]</h3>
<p>The second issue is of the amount of training data available relative to the complexity of the "true" function (classifier or regression function). If the true function is simple, then an "inflexible" learning algorithm with high bias and low variance will be able to learn it from a small amount of data. But if the true function is highly complex (e.g., because it involves complex interactions among many different input features and behaves differently in different parts of the input space), then the function will only be able to learn with a large amount of training data paired with a "flexible" learning algorithm with low bias and high variance.
</p>
<h3>Dimensionality of the input space[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=5">edit</a>]</h3>
<p>A third issue is the dimensionality of the input space. If the input feature vectors have large dimensions, learning the function can be difficult even if the true function only depends on a small number of those features. This is because the many "extra" dimensions can confuse the learning algorithm and cause it to have high variance. Hence, input data of large dimensions typically requires tuning the classifier to have low variance and high bias. In practice, if the engineer can manually remove irrelevant features from the input data, it will likely improve the accuracy of the learned function. In addition, there are many algorithms for <a href="/wiki/Feature_selection">feature selection</a> that seek to identify the relevant features and discard the irrelevant ones. This is an instance of the more general strategy of <a href="/wiki/Dimensionality_reduction">dimensionality reduction</a>, which seeks to map the input data into a lower-dimensional space prior to running the supervised learning algorithm.
</p>
<h3>Noise in the output values[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=6">edit</a>]</h3>
<p>A fourth issue is the degree of noise in the desired output values (the supervisory <a href="/wiki/Target_variable">target variables</a>). If the desired output values are often incorrect (because of human error or sensor errors), then the learning algorithm should not attempt to find a function that exactly matches the training examples. Attempting to fit the data too carefully leads to <a href="/wiki/Overfitting">overfitting</a>. You can overfit even when there are no measurement errors (stochastic noise) if the function you are trying to learn is too complex for your learning model. In such a situation, the part of the target function that cannot be modeled "corrupts" your training data - this phenomenon has been called <a href="/wiki/Deterministic_noise">deterministic noise</a>. When either type of noise is present, it is better to go with a higher bias, lower variance estimator.
</p><p>In practice, there are several approaches to alleviate noise in the output values such as <a href="/wiki/Early_stopping">early stopping</a> to prevent <a href="/wiki/Overfitting">overfitting</a> as well as <a href="/wiki/Anomaly_detection">detecting</a> and removing the noisy training examples prior to training the supervised learning algorithm. There are several algorithms that identify noisy training examples and removing the suspected noisy training examples prior to training has decreased <a href="/wiki/Generalization_error">generalization error</a> with <a href="/wiki/Statistical_significance">statistical significance</a>.<sup><a href="#cite_note-5">[5]</a></sup><sup><a href="#cite_note-6">[6]</a></sup>
</p>
<h3>Other factors to consider[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=7">edit</a>]</h3>
<p>Other factors to consider when choosing and applying a learning algorithm include the following:
</p>
<ul><li>Heterogeneity of the data. If the feature vectors include features of many different kinds (discrete, discrete ordered, counts, continuous values), some algorithms are easier to apply than others. Many algorithms, including <a href="/wiki/Support_Vector_Machines">support-vector machines</a>, <a href="/wiki/Linear_regression">linear regression</a>, <a href="/wiki/Logistic_regression">logistic regression</a>, <a href="/wiki/Artificial_neural_network">neural networks</a>, and <a href="/wiki/K-nearest_neighbor_algorithm">nearest neighbor methods</a>, require that the input features be numerical and scaled to similar ranges (e.g., to the [-1,1] interval). Methods that employ a distance function, such as <a href="/wiki/K-nearest_neighbor_algorithm">nearest neighbor methods</a> and <a href="/wiki/Support_Vector_Machines">support-vector machines with Gaussian kernels</a>, are particularly sensitive to this. An advantage of <a href="/wiki/Decision_tree_learning">decision trees</a> is that they easily handle heterogeneous data.</li>
<li>Redundancy in the data. If the input features contain redundant information (e.g., highly correlated features), some learning algorithms (e.g., <a href="/wiki/Linear_regression">linear regression</a>, <a href="/wiki/Logistic_regression">logistic regression</a>, and <a href="/wiki/K-nearest_neighbor_algorithm">distance based methods</a>) will perform poorly because of numerical instabilities. These problems can often be solved by imposing some form of <a href="/wiki/Regularization_(mathematics)">regularization</a>.</li>
<li>Presence of interactions and non-linearities. If each of the features makes an independent contribution to the output, then algorithms based on linear functions (e.g., <a href="/wiki/Linear_regression">linear regression</a>, <a href="/wiki/Logistic_regression">logistic regression</a>, <a href="/wiki/Support-vector_machine">support-vector machines</a>, <a href="/wiki/Naive_Bayes_classifier">naive Bayes</a>) and distance functions (e.g., <a href="/wiki/K-nearest_neighbor_algorithm">nearest neighbor methods</a>, <a href="/wiki/Support_Vector_Machines">support-vector machines with Gaussian kernels</a>) generally perform well. However, if there are complex interactions among features, then algorithms such as <a href="/wiki/Decision_tree_learning">decision trees</a> and <a href="/wiki/Artificial_neural_network">neural networks</a> work better, because they are specifically designed to discover these interactions. Linear methods can also be applied, but the engineer must manually specify the interactions when using them.</li></ul>
<p>When considering a new application, the engineer can compare multiple learning algorithms and experimentally determine which one works best on the problem at hand (see <a href="/wiki/Cross-validation_(statistics)">cross validation</a>). Tuning the performance of a learning algorithm can be very time-consuming. Given fixed resources, it is often better to spend more time collecting additional training data and more informative features than it is to spend extra time tuning the learning algorithms.
</p>
<h3>Algorithms[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=8">edit</a>]</h3>
<p>The most widely used learning algorithms are: 
</p>
<ul><li><a href="/wiki/Support-vector_machine">Support-vector machines</a></li>
<li><a href="/wiki/Linear_regression">Linear regression</a></li>
<li><a href="/wiki/Logistic_regression">Logistic regression</a></li>
<li><a href="/wiki/Naive_Bayes_classifier">Naive Bayes</a></li>
<li><a href="/wiki/Linear_discriminant_analysis">Linear discriminant analysis</a></li>
<li><a href="/wiki/Decision_tree_learning">Decision trees</a></li>
<li><a href="/wiki/K-nearest_neighbor_algorithm">K-nearest neighbor algorithm</a></li>
<li><a href="/wiki/Artificial_neural_network">Neural networks</a> (<a href="/wiki/Multilayer_perceptron">Multilayer perceptron</a>)</li>
<li><a href="/wiki/Similarity_learning">Similarity learning</a></li></ul>
<h2>How supervised learning algorithms work[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=9">edit</a>]</h2>
<p>Given a set of training examples of the form such that is the <a href="/wiki/Feature_vector">feature vector</a> of the -th example and is its label (i.e., class), a learning algorithm seeks a function , where is the input space and is the output space. The function is an element of some space of possible functions , usually called the <i>hypothesis space</i>. It is sometimes convenient to represent using a scoring function such that is defined as returning the value that gives the highest score: . Let denote the space of scoring functions.
</p><p>Although and can be any space of functions, many learning algorithms are probabilistic models where takes the form of a <a href="/wiki/Conditional_probability">conditional probability</a> model , or takes the form of a <a href="/wiki/Joint_probability">joint probability</a> model . For example, <a href="/wiki/Naive_Bayes_classifier">naive Bayes</a> and <a href="/wiki/Linear_discriminant_analysis">linear discriminant analysis</a> are joint probability models, whereas <a href="/wiki/Logistic_regression">logistic regression</a> is a conditional probability model.
</p><p>There are two basic approaches to choosing or : <a href="/wiki/Empirical_risk_minimization">empirical risk minimization</a> and <a href="/wiki/Structural_risk_minimization">structural risk minimization</a>.<sup><a href="#cite_note-7">[7]</a></sup> Empirical risk minimization seeks the function that best fits the training data. Structural risk minimization includes a <i>penalty function</i> that controls the bias/variance tradeoff.
</p><p>In both cases, it is assumed that the training set consists of a sample of <a href="/wiki/Independent_and_identically-distributed_random_variables">independent and identically distributed pairs</a>, . In order to measure how well a function fits the training data, a <a href="/wiki/Loss_function">loss function</a> is defined. For training example , the loss of predicting the value is .
</p><p>The <i>risk</i> of function is defined as the expected loss of . This can be estimated from the training data as
</p>
<dl><dd>.</dd></dl>
<h3>Empirical risk minimization[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=10">edit</a>]</h3>
<p>In empirical risk minimization, the supervised learning algorithm seeks the function that minimizes . Hence, a supervised learning algorithm can be constructed by applying an <a href="/wiki/Optimization_(mathematics)">optimization algorithm</a> to find .
</p><p>When is a conditional probability distribution and the loss function is the negative log likelihood: , then empirical risk minimization is equivalent to <a href="/wiki/Maximum_likelihood">maximum likelihood estimation</a>.
</p><p>When contains many candidate functions or the training set is not sufficiently large, empirical risk minimization leads to high variance and poor generalization. The learning algorithm is able to memorize the training examples without generalizing well. This is called <a href="/wiki/Overfitting">overfitting</a>.
</p>
<h3>Structural risk minimization[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=11">edit</a>]</h3>
<p><a href="/wiki/Structural_risk_minimization">Structural risk minimization</a> seeks to prevent overfitting by incorporating a <a href="/wiki/Regularization_(mathematics)">regularization penalty</a> into the optimization. The regularization penalty can be viewed as implementing a form of <a href="/wiki/Occam%27s_razor">Occam's razor</a> that prefers simpler functions over more complex ones.
</p><p>A wide variety of penalties have been employed that correspond to different definitions of complexity. For example, consider the case where the function is a linear function of the form
</p>
<dl><dd>.</dd></dl>
<p>A popular regularization penalty is , which is the squared <a href="/wiki/Euclidean_norm">Euclidean norm</a> of the weights, also known as the norm. Other norms include the norm, , and the <a href="/wiki/Norm_(mathematics)#Hamming_distance_of_a_vector_from_zero">"norm"</a>, which is the number of non-zero s. The penalty will be denoted by .
</p><p>The supervised learning optimization problem is to find the function that minimizes
</p>
<dl><dd></dd></dl>
<p>The parameter controls the bias-variance tradeoff. When , this gives empirical risk minimization with low bias and high variance. When is large, the learning algorithm will have high bias and low variance. The value of can be chosen empirically via <a href="/wiki/Cross-validation_(statistics)">cross validation</a>.
</p><p>The complexity penalty has a Bayesian interpretation as the negative log prior probability of , , in which case is the <a href="/wiki/Posterior_probability">posterior probability</a> of .
</p>
<h2>Generative training[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=12">edit</a>]</h2>
<p>The training methods described above are <i>discriminative training</i> methods, because they seek to find a function that discriminates well between the different output values (see <a href="/wiki/Discriminative_model">discriminative model</a>). For the special case where is a <a href="/wiki/Joint_probability_distribution">joint probability distribution</a> and the loss function is the negative log likelihood a risk minimization algorithm is said to perform <i>generative training</i>, because can be regarded as a <a href="/wiki/Generative_model">generative model</a> that explains how the data were generated. Generative training algorithms are often simpler and more computationally efficient than discriminative training algorithms. In some cases, the solution can be computed in closed form as in <a href="/wiki/Naive_Bayes_classifier">naive Bayes</a> and <a href="/wiki/Linear_discriminant_analysis">linear discriminant analysis</a>.
</p>
<h2>Generalizations[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=13">edit</a>]</h2>
<p>There are several ways in which the standard supervised learning problem can be generalized:
</p>
<ul><li><a href="/wiki/Semi-supervised_learning">Semi-supervised learning</a>: In this setting, the desired output values are provided only for a subset of the training data. The remaining data is unlabeled.</li>
<li><a href="/wiki/Weak_supervision">Weak supervision</a>: In this setting, noisy, limited, or imprecise sources are used to provide supervision signal for labeling training data.</li>
<li><a href="/wiki/Active_learning_(machine_learning)">Active learning</a>: Instead of assuming that all of the training examples are given at the start, active learning algorithms interactively collect new examples, typically by making queries to a human user. Often, the queries are based on unlabeled data, which is a scenario that combines semi-supervised learning with active learning.</li>
<li><a href="/wiki/Structured_prediction">Structured prediction</a>: When the desired output value is a complex object, such as a parse tree or a labeled graph, then standard methods must be extended.</li>
<li><a href="/wiki/Learning_to_rank">Learning to rank</a>: When the input is a set of objects and the desired output is a ranking of those objects, then again the standard methods must be extended.</li></ul>
<h2>Approaches and algorithms[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=14">edit</a>]</h2>
<ul><li>Analytical learning</li>
<li><a href="/wiki/Artificial_neural_network">Artificial neural network</a></li>
<li><a href="/wiki/Backpropagation">Backpropagation</a></li>
<li><a href="/wiki/Boosting_(meta-algorithm)">Boosting (meta-algorithm)</a></li>
<li><a href="/wiki/Bayesian_statistics">Bayesian statistics</a></li>
<li><a href="/wiki/Case-based_reasoning">Case-based reasoning</a></li>
<li><a href="/wiki/Decision_tree_learning">Decision tree learning</a></li>
<li><a href="/wiki/Inductive_logic_programming">Inductive logic programming</a></li>
<li><a href="/wiki/Gaussian_process_regression">Gaussian process regression</a></li>
<li><a href="/wiki/Genetic_programming">Genetic programming</a></li>
<li><a href="/wiki/Group_method_of_data_handling">Group method of data handling</a></li>
<li><a href="/wiki/Variable_kernel_density_estimation#Use_for_statistical_classification">Kernel estimators</a></li>
<li><a href="/wiki/Learning_automaton">Learning automata</a></li>
<li><a href="/wiki/Learning_classifier_system">Learning classifier systems</a></li>
<li><a href="/wiki/Learning_vector_quantization">Learning vector quantization</a></li>
<li><a href="/wiki/Minimum_message_length">Minimum message length</a> (<a href="/wiki/Decision_tree">decision trees</a>, decision graphs, etc.)</li>
<li><a href="/wiki/Multilinear_subspace_learning">Multilinear subspace learning</a></li>
<li><a href="/wiki/Naive_Bayes_classifier">Naive Bayes classifier</a></li>
<li><a href="/wiki/Maximum_entropy_classifier">Maximum entropy classifier</a></li>
<li><a href="/wiki/Conditional_random_field">Conditional random field</a></li>
<li><a href="/wiki/Nearest_neighbor_(pattern_recognition)">Nearest neighbor algorithm</a></li>
<li><a href="/wiki/Probably_approximately_correct_learning">Probably approximately correct learning</a> (PAC) learning</li>
<li><a href="/wiki/Ripple_down_rules">Ripple down rules</a>, a knowledge acquisition methodology</li>
<li>Symbolic machine learning algorithms</li>
<li>Subsymbolic machine learning algorithms</li>
<li><a href="/wiki/Support_vector_machine">Support vector machines</a></li>
<li>Minimum complexity machines (MCM)</li>
<li><a href="/wiki/Random_forest">Random forests</a></li>
<li><a href="/wiki/Ensembles_of_classifiers">Ensembles of classifiers</a></li>
<li><a href="/wiki/Ordinal_classification">Ordinal classification</a></li>
<li><a href="/wiki/Data_pre-processing">Data pre-processing</a></li>
<li>Handling imbalanced datasets</li>
<li><a href="/wiki/Statistical_relational_learning">Statistical relational learning</a></li>
<li><a href="/wiki/Proaftn">Proaftn</a>, a multicriteria classification algorithm</li></ul>
<h2>Applications[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=15">edit</a>]</h2>
<ul><li><a href="/wiki/Bioinformatics">Bioinformatics</a></li>
<li><a href="/wiki/Cheminformatics">Cheminformatics</a>
<ul><li><a href="/wiki/Quantitative_structure%E2%80%93activity_relationship">Quantitative structure–activity relationship</a></li></ul></li>
<li><a href="/wiki/Database_marketing">Database marketing</a></li>
<li><a href="/wiki/Handwriting_recognition">Handwriting recognition</a></li>
<li><a href="/wiki/Information_retrieval">Information retrieval</a>
<ul><li><a href="/wiki/Learning_to_rank">Learning to rank</a></li></ul></li>
<li><a href="/wiki/Information_extraction">Information extraction</a></li>
<li>Object recognition in <a href="/wiki/Computer_vision">computer vision</a></li>
<li><a href="/wiki/Optical_character_recognition">Optical character recognition</a></li>
<li><a href="/wiki/Spamming">Spam detection</a></li>
<li><a href="/wiki/Pattern_recognition">Pattern recognition</a></li>
<li><a href="/wiki/Speech_recognition">Speech recognition</a></li>
<li>Supervised learning is a special case of <a href="/wiki/Downward_causation">downward causation</a> in biological systems</li>
<li>Landform classification using <a href="/wiki/Satellite_imagery">satellite imagery</a><sup><a href="#cite_note-8">[8]</a></sup></li>
<li>Spend classification in <a href="/wiki/Procurement">procurement</a> processes<sup><a href="#cite_note-9">[9]</a></sup></li></ul>
<h2>General issues[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=16">edit</a>]</h2>
<ul><li><a href="/wiki/Computational_learning_theory">Computational learning theory</a></li>
<li><a href="/wiki/Inductive_bias">Inductive bias</a></li>
<li><a href="/wiki/Overfitting_(machine_learning)">Overfitting (machine learning)</a></li>
<li>(Uncalibrated) <a href="/wiki/Class_membership_probabilities">class membership probabilities</a></li>
<li><a href="/wiki/Unsupervised_learning">Unsupervised learning</a></li>
<li><a href="/wiki/Version_space">Version spaces</a></li></ul>
<h2>See also[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=17">edit</a>]</h2>
<ul><li><a href="/wiki/List_of_datasets_for_machine_learning_research">List of datasets for machine learning research</a></li></ul>
<h2>References[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=18">edit</a>]</h2>
<div><ol>
<li><b><a href="#cite_ref-1">^</a></b> Stuart J. Russell, Peter Norvig (2010) <i><a href="/wiki/Artificial_Intelligence:_A_Modern_Approach">Artificial Intelligence: A Modern Approach</a>, Third Edition</i>, Prentice Hall <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780136042594">9780136042594</a>.
</li>
<li><b><a href="#cite_ref-2">^</a></b> <a href="/wiki/Mehryar_Mohri">Mehryar Mohri</a>, Afshin Rostamizadeh, Ameet Talwalkar (2012) <i>Foundations of Machine Learning</i>, The MIT Press <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780262018258">9780262018258</a>.
</li>
<li><b><a href="#cite_ref-3">^</a></b> S. Geman, E. Bienenstock, and R. Doursat (1992). <a href="http://delta-apache-vm.cs.tau.ac.il/~nin/Courses/NC06/VarbiasBiasGeman.pdf">Neural networks and the bias/variance dilemma</a>. Neural Computation 4, 1–58.
</li>
<li><b><a href="#cite_ref-4">^</a></b> G. James (2003) Variance and Bias for General Loss Functions, Machine Learning 51, 115-135. (<a href="http://www-bcf.usc.edu/~gareth/research/bv.pdf">http://www-bcf.usc.edu/~gareth/research/bv.pdf</a>)
</li>
<li><b><a href="#cite_ref-5">^</a></b> C.E. Brodely and M.A. Friedl (1999). Identifying and Eliminating Mislabeled Training Instances, Journal of Artificial Intelligence Research 11, 131-167. (<a href="http://jair.org/media/606/live-606-1803-jair.pdf">http://jair.org/media/606/live-606-1803-jair.pdf</a>)
</li>
<li><b><a href="#cite_ref-6">^</a></b> <cite>M.R. Smith and T. Martinez (2011). "Improving Classification Accuracy by Identifying and Removing Instances that Should Be Misclassified". <i>Proceedings of International Joint Conference on Neural Networks (IJCNN 2011)</i>. pp. 2690–2697. <a href="/wiki/CiteSeerX_(identifier)">CiteSeerX</a> <a href="//citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.1371">10.1.1.221.1371</a>. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1109%2FIJCNN.2011.6033571">10.1109/IJCNN.2011.6033571</a>.</cite>
</li>
<li><b><a href="#cite_ref-7">^</a></b> Vapnik, V. N. <a href="https://books.google.com/books?id=EqgACAAAQBAJ&amp;printsec=frontcover#v=snippet&amp;q=%22empirical%20risk%20minimization%22%20OR%20%22structural%20risk%20minimization%22&amp;f=false">The Nature of Statistical Learning Theory</a> (2nd Ed.), Springer Verlag, 2000.
</li>
<li><b><a href="#cite_ref-8">^</a></b> <cite>A. Maity (2016). "Supervised Classification of RADARSAT-2 Polarimetric Data for Different Land Features". <a href="/wiki/ArXiv_(identifier)">arXiv</a>:<a href="//arxiv.org/abs/1608.00501">1608.00501</a> [<a href="//arxiv.org/archive/cs.CV">cs.CV</a>].</cite>
</li>
<li><b><a href="#cite_ref-9">^</a></b> <cite><a href="https://publication.sipmm.edu.sg/key-technologies-agile-procurement/">"Key Technologies for Agile Procurement | SIPMM Publications"</a>. <i>publication.sipmm.edu.sg</i>. 2020-10-09. Retrieved 2022-06-16.</cite>
</li>
</ol></div>
<h2>External links[<a href="/w/index.php?title=Supervised_learning&amp;action=edit&amp;section=19">edit</a>]</h2>
<ul><li><a href="http://www.mloss.org/">Machine Learning Open Source Software (MLOSS)</a></li></ul>
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 Contents

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 * (Top)
 * 1 Steps to follow
 * 2 Algorithm choice
 + 2.1 Bias-variance tradeoff
 + 2.2 Function complexity and amount of training data
 + 2.3 Dimensionality of the input space
 + 2.4 Noise in the output values
 + 2.5 Other factors to consider
 + 2.6 Algorithms
 * 3 How supervised learning algorithms work
 + 3.1 Empirical risk minimization
 + 3.2 Structural risk minimization
 * 4 Generative training
 * 5 Generalizations
 * 6 Approaches and algorithms
 * 7 Applications
 * 8 General issues
 * 9 See also
 * 10 References
 * 11 External links
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 Supervised learning

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 From Wikipedia, the free encyclopedia
 Part of a series on 
 Machine learning 
 and data mining 
  
 Paradigms 
 * Supervised learning 
 * Unsupervised learning 
 * Online learning 
 * Batch learning 
 * Semi-supervised learning 
 * Self-supervised learning 
 * Reinforcement learning 
 Problems 
 * Classification 
 * Regression 
 * Clustering 
 * dimension reduction 
 * density estimation 
 * Anomaly detection 
 * Data Cleaning 
 * AutoML 
 * Association rules 
 * Structured prediction 
 * Feature engineering 
 * Feature learning 
 * Learning to rank 
 * Grammar induction 
 Supervised learning 
 ( classification • regression ) 
 * Decision trees 
 * Ensembles 
 + Bagging 
 + Boosting 
 + Random forest 
 * k-NN 
 * Linear regression 
 * Naive Bayes 
 * Artificial neural networks 
 * Logistic regression 
 * Perceptron 
 * Relevance vector machine (RVM) 
 * Support vector machine (SVM) 
 Clustering 
 * BIRCH 
 * CURE 
 * Hierarchical 
 * k-means 
 * Fuzzy 
 * Expectation–maximization (EM) 
  
 * DBSCAN 
 * OPTICS 
 * Mean shift 
 Dimensionality reduction 
 * Factor analysis 
 * CCA 
 * ICA 
 * LDA 
 * NMF 
 * PCA 
 * PGD 
 * t-SNE 
 * SDL 
 Structured prediction 
 * Graphical models 
 + Bayes net 
 + Conditional random field 
 + Hidden Markov 
 Anomaly detection 
 * RANSAC 
 * k-NN 
 * Local outlier factor 
 * Isolation forest 
 Artificial neural network 
 * Autoencoder 
 * Cognitive computing 
 * Deep learning 
 * DeepDream 
 * Multilayer perceptron 
 * RNN 
 + LSTM 
 + GRU 
 + ESN 
 + reservoir computing 
 * Restricted Boltzmann machine 
 * GAN 
 * SOM 
 * Convolutional neural network 
 + U-Net 
 * Transformer 
 + Vision 
 * Spiking neural network 
 * Memtransistor 
 * Electrochemical RAM (ECRAM) 
 Reinforcement learning 
 * Q-learning 
 * SARSA 
 * Temporal difference (TD) 
 * Multi-agent 
 + Self-play 
 Learning with humans 
 * Active learning 
 * Crowdsourcing 
 * Human-in-the-loop 
 Model diagnostics 
 * Learning curve 
 Theory 
 * Kernel machines 
 * Bias–variance tradeoff 
 * Computational learning theory 
 * Empirical risk minimization 
 * Occam learning 
 * PAC learning 
 * Statistical learning 
 * VC theory 
 Machine-learning venues 
 * NeurIPS 
 * ICML 
 * ICLR 
 * ML 
 * JMLR 
 Related articles 
 * Glossary of artificial intelligence 
 * List of datasets for machine-learning research
 * Outline of machine learning 
 * v 
 * t 
 * e 
 
 See also: Unsupervised learning

 Supervised learning (SL) is a machine learning paradigm for problems where the available data consists of labelled examples, meaning that each data point contains features (covariates) and an associated label. The goal of supervised learning algorithms is learning a function that maps feature vectors (inputs) to labels (output), based on example input-output pairs.[1] It infers a function from labeled training data consisting of a set of training examples.[2] In supervised learning, each example is a pair consisting of an input object (typically a vector) and a desired output value (also called the supervisory signal). A supervised learning algorithm analyzes the training data and produces an inferred function, which can be used for mapping new examples. An optimal scenario will allow for the algorithm to correctly determine the class labels for unseen instances. This requires the learning algorithm to generalize from the training data to unseen situations in a "reasonable" way (see inductive bias). This statistical quality of an algorithm is measured through the so-called generalization error.

 Steps to follow [ edit ]

 To solve a given problem of supervised learning, one has to perform the following steps:

 1. Determine the type of training examples. Before doing anything else, the user should decide what kind of data is to be used as a training set. In the case of handwriting analysis, for example, this might be a single handwritten character, an entire handwritten word, an entire sentence of handwriting or perhaps a full paragraph of handwriting.
 2. Gather a training set. The training set needs to be representative of the real-world use of the function. Thus, a set of input objects is gathered and corresponding outputs are also gathered, either from human experts or from measurements.
 3. Determine the input feature representation of the learned function. The accuracy of the learned function depends strongly on how the input object is represented. Typically, the input object is transformed into a feature vector, which contains a number of features that are descriptive of the object. The number of features should not be too large, because of the curse of dimensionality; but should contain enough information to accurately predict the output.
 4. Determine the structure of the learned function and corresponding learning algorithm. For example, the engineer may choose to use support-vector machines or decision trees.
 5. Complete the design. Run the learning algorithm on the gathered training set. Some supervised learning algorithms require the user to determine certain control parameters. These parameters may be adjusted by optimizing performance on a subset (called a validation set) of the training set, or via cross-validation.
 6. Evaluate the accuracy of the learned function. After parameter adjustment and learning, the performance of the resulting function should be measured on a test set that is separate from the training set.

 Algorithm choice [ edit ]

 A wide range of supervised learning algorithms are available, each with its strengths and weaknesses. There is no single learning algorithm that works best on all supervised learning problems (see the No free lunch theorem).

 There are four major issues to consider in supervised learning:

 Bias-variance tradeoff [ edit ]

 Main article: Bias-variance dilemma

 A first issue is the tradeoff between bias and variance.[3] Imagine that we have available several different, but equally good, training data sets. A learning algorithm is biased for a particular input if, when trained on each of these data sets, it is systematically incorrect when predicting the correct output for . A learning algorithm has high variance for a particular input if it predicts different output values when trained on different training sets. The prediction error of a learned classifier is related to the sum of the bias and the variance of the learning algorithm.[4] Generally, there is a tradeoff between bias and variance. A learning algorithm with low bias must be "flexible" so that it can fit the data well. But if the learning algorithm is too flexible, it will fit each training data set differently, and hence have high variance. A key aspect of many supervised learning methods is that they are able to adjust this tradeoff between bias and variance (either automatically or by providing a bias/variance parameter that the user can adjust).

 Function complexity and amount of training data [ edit ]

 The second issue is of the amount of training data available relative to the complexity of the "true" function (classifier or regression function). If the true function is simple, then an "inflexible" learning algorithm with high bias and low variance will be able to learn it from a small amount of data. But if the true function is highly complex (e.g., because it involves complex interactions among many different input features and behaves differently in different parts of the input space), then the function will only be able to learn with a large amount of training data paired with a "flexible" learning algorithm with low bias and high variance.

 Dimensionality of the input space [ edit ]

 A third issue is the dimensionality of the input space. If the input feature vectors have large dimensions, learning the function can be difficult even if the true function only depends on a small number of those features. This is because the many "extra" dimensions can confuse the learning algorithm and cause it to have high variance. Hence, input data of large dimensions typically requires tuning the classifier to have low variance and high bias. In practice, if the engineer can manually remove irrelevant features from the input data, it will likely improve the accuracy of the learned function. In addition, there are many algorithms for feature selection that seek to identify the relevant features and discard the irrelevant ones. This is an instance of the more general strategy of dimensionality reduction, which seeks to map the input data into a lower-dimensional space prior to running the supervised learning algorithm.

 Noise in the output values [ edit ]

 A fourth issue is the degree of noise in the desired output values (the supervisory target variables). If the desired output values are often incorrect (because of human error or sensor errors), then the learning algorithm should not attempt to find a function that exactly matches the training examples. Attempting to fit the data too carefully leads to overfitting. You can overfit even when there are no measurement errors (stochastic noise) if the function you are trying to learn is too complex for your learning model. In such a situation, the part of the target function that cannot be modeled "corrupts" your training data - this phenomenon has been called deterministic noise. When either type of noise is present, it is better to go with a higher bias, lower variance estimator.

 In practice, there are several approaches to alleviate noise in the output values such as early stopping to prevent overfitting as well as detecting and removing the noisy training examples prior to training the supervised learning algorithm. There are several algorithms that identify noisy training examples and removing the suspected noisy training examples prior to training has decreased generalization error with statistical significance.[5][6]

 Other factors to consider [ edit ]

 Other factors to consider when choosing and applying a learning algorithm include the following:

 * Heterogeneity of the data. If the feature vectors include features of many different kinds (discrete, discrete ordered, counts, continuous values), some algorithms are easier to apply than others. Many algorithms, including support-vector machines, linear regression, logistic regression, neural networks, and nearest neighbor methods, require that the input features be numerical and scaled to similar ranges (e.g., to the [-1,1] interval). Methods that employ a distance function, such as nearest neighbor methods and support-vector machines with Gaussian kernels, are particularly sensitive to this. An advantage of decision trees is that they easily handle heterogeneous data.
 * Redundancy in the data. If the input features contain redundant information (e.g., highly correlated features), some learning algorithms (e.g., linear regression, logistic regression, and distance based methods) will perform poorly because of numerical instabilities. These problems can often be solved by imposing some form of regularization.
 * Presence of interactions and non-linearities. If each of the features makes an independent contribution to the output, then algorithms based on linear functions (e.g., linear regression, logistic regression, support-vector machines, naive Bayes) and distance functions (e.g., nearest neighbor methods, support-vector machines with Gaussian kernels) generally perform well. However, if there are complex interactions among features, then algorithms such as decision trees and neural networks work better, because they are specifically designed to discover these interactions. Linear methods can also be applied, but the engineer must manually specify the interactions when using them.

 When considering a new application, the engineer can compare multiple learning algorithms and experimentally determine which one works best on the problem at hand (see cross validation). Tuning the performance of a learning algorithm can be very time-consuming. Given fixed resources, it is often better to spend more time collecting additional training data and more informative features than it is to spend extra time tuning the learning algorithms.

 Algorithms [ edit ]

 The most widely used learning algorithms are:

 * Support-vector machines
 * Linear regression
 * Logistic regression
 * Naive Bayes
 * Linear discriminant analysis
 * Decision trees
 * K-nearest neighbor algorithm
 * Neural networks (Multilayer perceptron)
 * Similarity learning

 How supervised learning algorithms work [ edit ]

 Given a set of training examples of the form such that is the feature vector of the -th example and is its label (i.e., class), a learning algorithm seeks a function , where is the input space and is the output space. The function is an element of some space of possible functions , usually called the hypothesis space. It is sometimes convenient to represent using a scoring function such that is defined as returning the value that gives the highest score: . Let denote the space of scoring functions.

 Although and can be any space of functions, many learning algorithms are probabilistic models where takes the form of a conditional probability model , or takes the form of a joint probability model . For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model.

 There are two basic approaches to choosing or : empirical risk minimization and structural risk minimization.[7] Empirical risk minimization seeks the function that best fits the training data. Structural risk minimization includes a penalty function that controls the bias/variance tradeoff.

 In both cases, it is assumed that the training set consists of a sample of independent and identically distributed pairs, . In order to measure how well a function fits the training data, a loss function is defined. For training example , the loss of predicting the value is .

 The risk of function is defined as the expected loss of . This can be estimated from the training data as

 .

 Empirical risk minimization [ edit ]

 Main article: Empirical risk minimization

 In empirical risk minimization, the supervised learning algorithm seeks the function that minimizes . Hence, a supervised learning algorithm can be constructed by applying an optimization algorithm to find .

 When is a conditional probability distribution and the loss function is the negative log likelihood: , then empirical risk minimization is equivalent to maximum likelihood estimation.

 When contains many candidate functions or the training set is not sufficiently large, empirical risk minimization leads to high variance and poor generalization. The learning algorithm is able to memorize the training examples without generalizing well. This is called overfitting.

 Structural risk minimization [ edit ]

 Structural risk minimization seeks to prevent overfitting by incorporating a regularization penalty into the optimization. The regularization penalty can be viewed as implementing a form of Occam's razor that prefers simpler functions over more complex ones.

 A wide variety of penalties have been employed that correspond to different definitions of complexity. For example, consider the case where the function is a linear function of the form

 .

 A popular regularization penalty is , which is the squared Euclidean norm of the weights, also known as the norm. Other norms include the norm, , and the "norm", which is the number of non-zero s. The penalty will be denoted by .

 The supervised learning optimization problem is to find the function that minimizes

 The parameter controls the bias-variance tradeoff. When , this gives empirical risk minimization with low bias and high variance. When is large, the learning algorithm will have high bias and low variance. The value of can be chosen empirically via cross validation.

 The complexity penalty has a Bayesian interpretation as the negative log prior probability of , , in which case is the posterior probability of .

 Generative training [ edit ]

 The training methods described above are discriminative training methods, because they seek to find a function that discriminates well between the different output values (see discriminative model). For the special case where is a joint probability distribution and the loss function is the negative log likelihood a risk minimization algorithm is said to perform generative training, because can be regarded as a generative model that explains how the data were generated. Generative training algorithms are often simpler and more computationally efficient than discriminative training algorithms. In some cases, the solution can be computed in closed form as in naive Bayes and linear discriminant analysis.

 Generalizations [ edit ]

 There are several ways in which the standard supervised learning problem can be generalized:

 * Semi-supervised learning: In this setting, the desired output values are provided only for a subset of the training data. The remaining data is unlabeled.
 * Weak supervision: In this setting, noisy, limited, or imprecise sources are used to provide supervision signal for labeling training data.
 * Active learning: Instead of assuming that all of the training examples are given at the start, active learning algorithms interactively collect new examples, typically by making queries to a human user. Often, the queries are based on unlabeled data, which is a scenario that combines semi-supervised learning with active learning.
 * Structured prediction: When the desired output value is a complex object, such as a parse tree or a labeled graph, then standard methods must be extended.
 * Learning to rank: When the input is a set of objects and the desired output is a ranking of those objects, then again the standard methods must be extended.

 Approaches and algorithms [ edit ]

 * Analytical learning
 * Artificial neural network
 * Backpropagation
 * Boosting (meta-algorithm)
 * Bayesian statistics
 * Case-based reasoning
 * Decision tree learning
 * Inductive logic programming
 * Gaussian process regression
 * Genetic programming
 * Group method of data handling
 * Kernel estimators
 * Learning automata
 * Learning classifier systems
 * Learning vector quantization
 * Minimum message length (decision trees, decision graphs, etc.)
 * Multilinear subspace learning
 * Naive Bayes classifier
 * Maximum entropy classifier
 * Conditional random field
 * Nearest neighbor algorithm
 * Probably approximately correct learning (PAC) learning
 * Ripple down rules, a knowledge acquisition methodology
 * Symbolic machine learning algorithms
 * Subsymbolic machine learning algorithms
 * Support vector machines
 * Minimum complexity machines (MCM)
 * Random forests
 * Ensembles of classifiers
 * Ordinal classification
 * Data pre-processing
 * Handling imbalanced datasets
 * Statistical relational learning
 * Proaftn, a multicriteria classification algorithm

 Applications [ edit ]

 * Bioinformatics
 * Cheminformatics
 + Quantitative structure–activity relationship
 * Database marketing
 * Handwriting recognition
 * Information retrieval
 + Learning to rank
 * Information extraction
 * Object recognition in computer vision
 * Optical character recognition
 * Spam detection
 * Pattern recognition
 * Speech recognition
 * Supervised learning is a special case of downward causation in biological systems
 * Landform classification using satellite imagery[8]
 * Spend classification in procurement processes[9]

 General issues [ edit ]

 * Computational learning theory
 * Inductive bias
 * Overfitting (machine learning)
 * (Uncalibrated) class membership probabilities
 * Unsupervised learning
 * Version spaces

 See also [ edit ]

 * List of datasets for machine learning research

 References [ edit ]

 1. ^ Stuart J. Russell, Peter Norvig (2010) Artificial Intelligence: A Modern Approach, Third Edition , Prentice Hall ISBN 9780136042594 .
 2. ^ Mehryar Mohri , Afshin Rostamizadeh, Ameet Talwalkar (2012) Foundations of Machine Learning , The MIT Press ISBN 9780262018258 .
 3. ^ S. Geman, E. Bienenstock, and R. Doursat (1992). Neural networks and the bias/variance dilemma . Neural Computation 4, 1–58.
 4. ^ G. James (2003) Variance and Bias for General Loss Functions, Machine Learning 51, 115-135. ( http://www-bcf.usc.edu/~gareth/research/bv.pdf )
 5. ^ C.E. Brodely and M.A. Friedl (1999). Identifying and Eliminating Mislabeled Training Instances, Journal of Artificial Intelligence Research 11, 131-167. ( http://jair.org/media/606/live-606-1803-jair.pdf )
 6. ^ M.R. Smith and T. Martinez (2011). "Improving Classification Accuracy by Identifying and Removing Instances that Should Be Misclassified". Proceedings of International Joint Conference on Neural Networks (IJCNN 2011). pp. 2690–2697. CiteSeerX 10.1.1.221.1371. doi:10.1109/IJCNN.2011.6033571.
 7. ^ Vapnik, V. N. The Nature of Statistical Learning Theory (2nd Ed.), Springer Verlag, 2000.
 8. ^ A. Maity (2016). "Supervised Classification of RADARSAT-2 Polarimetric Data for Different Land Features". arXiv:1608.00501 [cs.CV].
 9. ^ "Key Technologies for Agile Procurement | SIPMM Publications". publication.sipmm.edu.sg. 2020-10-09 . Retrieved 2022-06-16 .

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From Wikipedia, the free encyclopedia
	 
 Supervised learning (SL) is a machine learning paradigm for problems where the available data consists of labelled examples, meaning that each data point contains features (covariates) and an associated label. The goal of supervised learning algorithms is learning a function that maps feature vectors (inputs) to labels (output), based on example input-output pairs. [1]  It infers a function from labeled training data  consisting of a set of training examples. [2]  In supervised learning, each example is a pair consisting of an input object (typically a vector) and a desired output value (also called the supervisory signal). A supervised learning algorithm analyzes the training data and produces an inferred function, which can be used for mapping new examples. An optimal scenario will allow for the algorithm to correctly determine the class labels for unseen instances. This requires the learning algorithm to generalize from the training data to unseen situations in a "reasonable" way (see inductive bias). This statistical quality of an algorithm is measured through the so-called generalization error.
Steps to follow[edit]
To solve a given problem of supervised learning, one has to perform the following steps:
 Determine the type of training examples. Before doing anything else, the user should decide what kind of data is to be used as a training set. In the case of handwriting analysis, for example, this might be a single handwritten character, an entire handwritten word, an entire sentence of handwriting or perhaps a full paragraph of handwriting.
Gather a training set. The training set needs to be representative of the real-world use of the function. Thus, a set of input objects is gathered and corresponding outputs are also gathered, either from human experts or from measurements.
Determine the input feature representation of the learned function. The accuracy of the learned function depends strongly on how the input object is represented. Typically, the input object is transformed into a feature vector, which contains a number of features that are descriptive of the object. The number of features should not be too large, because of the curse of dimensionality; but should contain enough information to accurately predict the output.
Determine the structure of the learned function and corresponding learning algorithm. For example, the engineer may choose to use support-vector machines or decision trees.
Complete the design. Run the learning algorithm on the gathered training set. Some supervised learning algorithms require the user to determine certain control parameters. These parameters may be adjusted by optimizing performance on a subset (called a validation set) of the training set, or via cross-validation.
Evaluate the accuracy of the learned function. After parameter adjustment and learning, the performance of the resulting function should be measured on a test set that is separate from the training set. 
Algorithm choice[edit]
A wide range of supervised learning algorithms are available, each with its strengths and weaknesses. There is no single learning algorithm that works best on all supervised learning problems (see the No free lunch theorem).
 There are four major issues to consider in supervised learning:
Bias-variance tradeoff[edit]
A first issue is the tradeoff between bias and variance. [3]  Imagine that we have available several different, but equally good, training data sets. A learning algorithm is biased for a particular input if, when trained on each of these data sets, it is systematically incorrect when predicting the correct output for . A learning algorithm has high variance for a particular input if it predicts different output values when trained on different training sets. The prediction error of a learned classifier is related to the sum of the bias and the variance of the learning algorithm. [4]  Generally, there is a tradeoff between bias and variance. A learning algorithm with low bias must be "flexible" so that it can fit the data well. But if the learning algorithm is too flexible, it will fit each training data set differently, and hence have high variance. A key aspect of many supervised learning methods is that they are able to adjust this tradeoff between bias and variance (either automatically or by providing a bias/variance parameter that the user can adjust).
Function complexity and amount of training data[edit]
The second issue is of the amount of training data available relative to the complexity of the "true" function (classifier or regression function). If the true function is simple, then an "inflexible" learning algorithm with high bias and low variance will be able to learn it from a small amount of data. But if the true function is highly complex (e.g., because it involves complex interactions among many different input features and behaves differently in different parts of the input space), then the function will only be able to learn with a large amount of training data paired with a "flexible" learning algorithm with low bias and high variance.
Dimensionality of the input space[edit]
A third issue is the dimensionality of the input space. If the input feature vectors have large dimensions, learning the function can be difficult even if the true function only depends on a small number of those features. This is because the many "extra" dimensions can confuse the learning algorithm and cause it to have high variance. Hence, input data of large dimensions typically requires tuning the classifier to have low variance and high bias. In practice, if the engineer can manually remove irrelevant features from the input data, it will likely improve the accuracy of the learned function. In addition, there are many algorithms for feature selection that seek to identify the relevant features and discard the irrelevant ones. This is an instance of the more general strategy of dimensionality reduction, which seeks to map the input data into a lower-dimensional space prior to running the supervised learning algorithm.
Noise in the output values[edit]
A fourth issue is the degree of noise in the desired output values (the supervisory target variables). If the desired output values are often incorrect (because of human error or sensor errors), then the learning algorithm should not attempt to find a function that exactly matches the training examples. Attempting to fit the data too carefully leads to overfitting. You can overfit even when there are no measurement errors (stochastic noise) if the function you are trying to learn is too complex for your learning model. In such a situation, the part of the target function that cannot be modeled "corrupts" your training data - this phenomenon has been called deterministic noise. When either type of noise is present, it is better to go with a higher bias, lower variance estimator.
 In practice, there are several approaches to alleviate noise in the output values such as early stopping to prevent overfitting as well as detecting and removing the noisy training examples prior to training the supervised learning algorithm. There are several algorithms that identify noisy training examples and removing the suspected noisy training examples prior to training has decreased generalization error with statistical significance. [5]   [6] 
Other factors to consider[edit]
Other factors to consider when choosing and applying a learning algorithm include the following:
 Heterogeneity of the data. If the feature vectors include features of many different kinds (discrete, discrete ordered, counts, continuous values), some algorithms are easier to apply than others. Many algorithms, including support-vector machines, linear regression, logistic regression, neural networks, and nearest neighbor methods, require that the input features be numerical and scaled to similar ranges (e.g., to the [-1,1] interval). Methods that employ a distance function, such as nearest neighbor methods and support-vector machines with Gaussian kernels, are particularly sensitive to this. An advantage of decision trees is that they easily handle heterogeneous data.
Redundancy in the data. If the input features contain redundant information (e.g., highly correlated features), some learning algorithms (e.g., linear regression, logistic regression, and distance based methods) will perform poorly because of numerical instabilities. These problems can often be solved by imposing some form of regularization.
Presence of interactions and non-linearities. If each of the features makes an independent contribution to the output, then algorithms based on linear functions (e.g., linear regression, logistic regression, support-vector machines, naive Bayes) and distance functions (e.g., nearest neighbor methods, support-vector machines with Gaussian kernels) generally perform well. However, if there are complex interactions among features, then algorithms such as decision trees and neural networks work better, because they are specifically designed to discover these interactions. Linear methods can also be applied, but the engineer must manually specify the interactions when using them. 
When considering a new application, the engineer can compare multiple learning algorithms and experimentally determine which one works best on the problem at hand (see cross validation). Tuning the performance of a learning algorithm can be very time-consuming. Given fixed resources, it is often better to spend more time collecting additional training data and more informative features than it is to spend extra time tuning the learning algorithms.
Algorithms[edit]
The most widely used learning algorithms are: 
  Support-vector machines 
 Linear regression 
 Logistic regression 
 Naive Bayes 
 Linear discriminant analysis 
 Decision trees 
 K-nearest neighbor algorithm 
 Neural networks (Multilayer perceptron)
 Similarity learning  
How supervised learning algorithms work[edit]
Given a set of training examples of the form such that is the feature vector of the -th example and is its label (i.e., class), a learning algorithm seeks a function , where is the input space and is the output space. The function is an element of some space of possible functions , usually called the hypothesis space. It is sometimes convenient to represent using a scoring function such that is defined as returning the value that gives the highest score: . Let denote the space of scoring functions.
 Although and can be any space of functions, many learning algorithms are probabilistic models where takes the form of a conditional probability model , or takes the form of a joint probability model . For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model.
 There are two basic approaches to choosing or : empirical risk minimization and structural risk minimization. [7]  Empirical risk minimization seeks the function that best fits the training data. Structural risk minimization includes a penalty function that controls the bias/variance tradeoff.
 In both cases, it is assumed that the training set consists of a sample of independent and identically distributed pairs, . In order to measure how well a function fits the training data, a loss function is defined. For training example , the loss of predicting the value is .
 The risk of function is defined as the expected loss of . This can be estimated from the training data as
 . 
Empirical risk minimization[edit]
In empirical risk minimization, the supervised learning algorithm seeks the function that minimizes . Hence, a supervised learning algorithm can be constructed by applying an optimization algorithm to find .
 When is a conditional probability distribution and the loss function is the negative log likelihood: , then empirical risk minimization is equivalent to maximum likelihood estimation.
 When contains many candidate functions or the training set is not sufficiently large, empirical risk minimization leads to high variance and poor generalization. The learning algorithm is able to memorize the training examples without generalizing well. This is called overfitting.
Structural risk minimization[edit]
 Structural risk minimization seeks to prevent overfitting by incorporating a regularization penalty into the optimization. The regularization penalty can be viewed as implementing a form of Occam's razor that prefers simpler functions over more complex ones.
 A wide variety of penalties have been employed that correspond to different definitions of complexity. For example, consider the case where the function is a linear function of the form
 . 
A popular regularization penalty is , which is the squared Euclidean norm of the weights, also known as the norm. Other norms include the norm, , and the "norm", which is the number of non-zero s. The penalty will be denoted by .
 The supervised learning optimization problem is to find the function that minimizes
   
The parameter controls the bias-variance tradeoff. When , this gives empirical risk minimization with low bias and high variance. When is large, the learning algorithm will have high bias and low variance. The value of can be chosen empirically via cross validation.
 The complexity penalty has a Bayesian interpretation as the negative log prior probability of , , in which case is the posterior probability of .
Generative training[edit]
The training methods described above are discriminative training methods, because they seek to find a function that discriminates well between the different output values (see discriminative model). For the special case where is a joint probability distribution and the loss function is the negative log likelihood a risk minimization algorithm is said to perform generative training, because can be regarded as a generative model that explains how the data were generated. Generative training algorithms are often simpler and more computationally efficient than discriminative training algorithms. In some cases, the solution can be computed in closed form as in naive Bayes and linear discriminant analysis.
Generalizations[edit]
There are several ways in which the standard supervised learning problem can be generalized:
  Semi-supervised learning: In this setting, the desired output values are provided only for a subset of the training data. The remaining data is unlabeled.
 Weak supervision: In this setting, noisy, limited, or imprecise sources are used to provide supervision signal for labeling training data.
 Active learning: Instead of assuming that all of the training examples are given at the start, active learning algorithms interactively collect new examples, typically by making queries to a human user. Often, the queries are based on unlabeled data, which is a scenario that combines semi-supervised learning with active learning.
 Structured prediction: When the desired output value is a complex object, such as a parse tree or a labeled graph, then standard methods must be extended.
 Learning to rank: When the input is a set of objects and the desired output is a ranking of those objects, then again the standard methods must be extended. 
Approaches and algorithms[edit]
 Analytical learning
 Artificial neural network 
 Backpropagation 
 Boosting (meta-algorithm) 
 Bayesian statistics 
 Case-based reasoning 
 Decision tree learning 
 Inductive logic programming 
 Gaussian process regression 
 Genetic programming 
 Group method of data handling 
 Kernel estimators 
 Learning automata 
 Learning classifier systems 
 Learning vector quantization 
 Minimum message length (decision trees, decision graphs, etc.)
 Multilinear subspace learning 
 Naive Bayes classifier 
 Maximum entropy classifier 
 Conditional random field 
 Nearest neighbor algorithm 
 Probably approximately correct learning (PAC) learning
 Ripple down rules, a knowledge acquisition methodology
Symbolic machine learning algorithms
Subsymbolic machine learning algorithms
 Support vector machines 
Minimum complexity machines (MCM)
 Random forests 
 Ensembles of classifiers 
 Ordinal classification 
 Data pre-processing 
Handling imbalanced datasets
 Statistical relational learning 
 Proaftn, a multicriteria classification algorithm 
Applications[edit]
  Bioinformatics 
 Cheminformatics
  Quantitative structure–activity relationship   
 Database marketing 
 Handwriting recognition 
 Information retrieval
  Learning to rank   
 Information extraction 
Object recognition in computer vision 
 Optical character recognition 
 Spam detection 
 Pattern recognition 
 Speech recognition 
Supervised learning is a special case of downward causation in biological systems
Landform classification using satellite imagery  [8]  
Spend classification in procurement processes [9]   
General issues[edit]
  Computational learning theory 
 Inductive bias 
 Overfitting (machine learning) 
(Uncalibrated) class membership probabilities 
 Unsupervised learning 
 Version spaces  
See also[edit]
  List of datasets for machine learning research  
References[edit]
 
  ^  Stuart J. Russell, Peter Norvig (2010)  Artificial Intelligence: A Modern Approach, Third Edition, Prentice Hall ISBN 9780136042594.
  ^  Mehryar Mohri, Afshin Rostamizadeh, Ameet Talwalkar (2012) Foundations of Machine Learning, The MIT Press ISBN 9780262018258.
  ^  S. Geman, E. Bienenstock, and R. Doursat (1992). Neural networks and the bias/variance dilemma. Neural Computation 4, 1–58.
  ^  G. James (2003) Variance and Bias for General Loss Functions, Machine Learning 51, 115-135. (http://www-bcf.usc.edu/~gareth/research/bv.pdf)
  ^  C.E. Brodely and M.A. Friedl (1999). Identifying and Eliminating Mislabeled Training Instances, Journal of Artificial Intelligence Research 11, 131-167. (http://jair.org/media/606/live-606-1803-jair.pdf)
  ^  M.R. Smith and T. Martinez (2011). "Improving Classification Accuracy by Identifying and Removing Instances that Should Be Misclassified". Proceedings of International Joint Conference on Neural Networks (IJCNN 2011). pp. 2690–2697. CiteSeerX 10.1.1.221.1371. doi:10.1109/IJCNN.2011.6033571.
  ^  Vapnik, V. N. The Nature of Statistical Learning Theory (2nd Ed.), Springer Verlag, 2000.
  ^  A. Maity (2016). "Supervised Classification of RADARSAT-2 Polarimetric Data for Different Land Features". arXiv:1608.00501 [cs.CV].
  ^   "Key Technologies for Agile Procurement | SIPMM Publications". publication.sipmm.edu.sg. 2020-10-09. Retrieved 2022-06-16.
 
External links[edit]
  Machine Learning Open Source Software (MLOSS)
Supervised learning - Wikipedia
https://en.wikipedia.org/wiki/Supervised_learning
https://en.wikipedia.org/wiki/Bias%E2%80%93variance_tradeoff
Bias–variance tradeoff - Wikipedia
2013-10-01
None
<div><div>
	<p>From Wikipedia, the free encyclopedia</p>
	</div><div>
<div><div><p><a href="/wiki/File:Test_function_and_noisy_data.png"></a></p><p>Function and noisy data</p></div><div><p><a href="/wiki/File:Radial_basis_function_fit,_spread%3D5.png"></a></p><p>Spread=5</p></div><div><p><a href="/wiki/File:Radial_basis_function_fit,_spread%3D1.png"></a></p><p>Spread=1</p></div><div><p><a href="/wiki/File:Radial_basis_function_fit,_spread%3D0.1.png"></a></p><p>Spread=0.1</p></div><div><p>A function (red) is approximated using <a href="/wiki/Radial_basis_functions">radial basis functions</a> (blue). Several trials are shown in each graph. For each trial, a few noisy data points are provided as a training set (top). For a wide spread (image 2) the bias is high: the RBFs cannot fully approximate the function (especially the central dip), but the variance between different trials is low. As spread decreases (image 3 and 4) the bias decreases: the blue curves more closely approximate the red. However, depending on the noise in different trials the variance between trials increases. In the lowermost image the approximated values for x=0 varies wildly depending on where the data points were located.</p></div></div>
<div><p><a href="/wiki/File:Bias_and_variance_contributing_to_total_error.svg"></a></p><div><p>Bias and variance as function of model complexity</p></div></div>
<p>In <a href="/wiki/Statistics">statistics</a> and <a href="/wiki/Machine_learning">machine learning</a>, the <b>bias–variance tradeoff</b> is the property of a model that the <a href="/wiki/Variance">variance</a> of the parameter estimated across <a href="/wiki/Sample_(statistics)">samples</a> can be reduced by increasing the <a href="/wiki/Bias_of_an_estimator">bias</a> in the <a href="/wiki/Estimation_theory">estimated</a> <a href="/wiki/Statistical_parameter">parameters</a>.
The <b>bias–variance dilemma</b> or <b>bias–variance problem</b> is the conflict in trying to simultaneously minimize these two sources of <a href="/wiki/Errors_and_residuals_in_statistics">error</a> that prevent <a href="/wiki/Supervised_learning">supervised learning</a> algorithms from generalizing beyond their <a href="/wiki/Training_set">training set</a>:<sup><a href="#cite_note-1">[1]</a></sup><sup><a href="#cite_note-2">[2]</a></sup>
</p>
<ul><li>The <a href="/wiki/Bias_of_an_estimator"><i>bias</i></a> error is an error from erroneous assumptions in the learning <a href="/wiki/Algorithm">algorithm</a>. High bias can cause an algorithm to miss the relevant relations between features and target outputs (underfitting).</li>
<li>The <i><a href="/wiki/Variance">variance</a></i> is an error from sensitivity to small fluctuations in the training set. High variance may result from an algorithm modeling the random <a href="/wiki/Noise_(signal_processing)">noise</a> in the training data (<a href="/wiki/Overfitting">overfitting</a>).</li></ul>
<p>The <b>bias–variance decomposition</b> is a way of analyzing a learning algorithm's <a href="/wiki/Expected_value">expected</a> <a href="/wiki/Generalization_error">generalization error</a> with respect to a particular problem as a sum of three terms, the bias, variance, and a quantity called the <i>irreducible error</i>, resulting from noise in the problem itself.
</p>
<h2>Motivation[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=1">edit</a>]</h2>
<ul>
	<li><div>
	<div><p><a href="/wiki/File:En_low_bias_low_variance.png"></a></p></div>
	<p>bias low, variance low
</p>
	</div></li>
	<li><div>
	<div><p><a href="/wiki/File:Truen_bad_prec_ok.png"></a></p></div>
	<p>bias high,<br />variance low
</p>
	</div></li>
	<li><div>
	<div><p><a href="/wiki/File:Truen_ok_prec_bad.png"></a></p></div>
	<p>bias low,<br />variance high
</p>
	</div></li>
	<li><div>
	<div><p><a href="/wiki/File:Truen_bad_prec_bad.png"></a></p></div>
	<p>bias high,<br />variance high
</p>
	</div></li>
</ul>
<p>The bias–variance tradeoff is a central problem in supervised learning. Ideally, one wants to <a href="/wiki/Model_selection">choose a model</a> that both accurately captures the regularities in its training data, but also <a href="/wiki/Generalization">generalizes</a> well to unseen data. Unfortunately, it is typically impossible to do both simultaneously. High-variance learning methods may be able to represent their training set well but are at risk of overfitting to noisy or unrepresentative training data. In contrast, algorithms with high bias typically produce simpler models that may fail to capture important regularities (i.e. underfit) in the data.
</p><p>It is an often made <a href="/wiki/Affirming_the_consequent">fallacy</a><sup><a href="#cite_note-nealThesis2019-3">[3]</a></sup><sup><a href="#cite_note-neal2018-4">[4]</a></sup> to assume that complex models must have high variance; High variance models are 'complex' in some sense, but the reverse needs not be true<sup>[<i><a href="/wiki/Wikipedia:Please_clarify">clarification needed</a></i>]</sup>.
In addition, one has to be careful how to define complexity: In particular, the number of parameters used to describe the model is a poor measure of complexity. This is illustrated by an example adapted from:<sup><a href="#cite_note-5">[5]</a></sup> The model has only two parameters () but it can interpolate any number of points by oscillating with a high enough frequency, resulting in both a high bias and high variance.
</p><p>An analogy can be made to the relationship between <a href="/wiki/Accuracy_and_precision">accuracy and precision</a>. Accuracy is a description of bias and can intuitively be improved by selecting from only <a href="/wiki/Sample_space">local</a> information. Consequently, a sample will appear accurate (i.e. have low bias) under the aforementioned selection conditions, but may result in underfitting. In other words, <a href="/wiki/Training,_validation,_and_test_data_sets">test data</a> may not agree as closely with training data, which would indicate imprecision and therefore inflated variance. A graphical example would be a straight line fit to data exhibiting quadratic behavior overall. Precision is a description of variance and generally can only be improved by selecting information from a comparatively larger space. The option to select many data points over a broad sample space is the ideal condition for any analysis. However, intrinsic constraints (whether physical, theoretical, computational, etc.) will always play a limiting role. The limiting case where only a finite number of data points are selected over a broad sample space may result in improved precision and lower variance overall, but may also result in an overreliance on the training data (overfitting). This means that test data would also not agree as closely with the training data, but in this case the reason is due to inaccuracy or high bias. To borrow from the previous example, the graphical representation would appear as a high-order polynomial fit to the same data exhibiting quadratic behavior. Note that error in each case is measured the same way, but the reason ascribed to the error is different depending on the balance between bias and variance. To mitigate how much information is used from neighboring observations, a model can be <a href="/wiki/Smoothing">smoothed</a> via explicit <a href="/wiki/Regularization_(mathematics)">regularization</a>, such as <a href="/wiki/Shrinkage_(statistics)">shrinkage</a>.
</p>
<h2>Bias–variance decomposition of mean squared error[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=2">edit</a>]</h2>
<p>Suppose that we have a training set consisting of a set of points and real values associated with each point . We assume that there is a function f(x) such as , where the noise, , has zero mean and variance .
</p><p>We want to find a function , that approximates the true function as well as possible, by means of some learning algorithm based on a training dataset (sample) . We make "as well as possible" precise by measuring the <a href="/wiki/Mean_squared_error">mean squared error</a> between and : we want to be minimal, both for <i>and for points outside of our sample</i>. Of course, we cannot hope to do so perfectly, since the contain noise ; this means we must be prepared to accept an <i>irreducible error</i> in any function we come up with.
</p><p>Finding an that generalizes to points outside of the training set can be done with any of the countless algorithms used for supervised learning. It turns out that whichever function we select, we can decompose its <a href="/wiki/Expected_value">expected</a> error on an unseen sample as follows:<sup><a href="#cite_note-islr-6">[6]</a></sup><sup>: 34 </sup><sup><a href="#cite_note-ESL-7">[7]</a></sup><sup>: 223 </sup>
</p>
<dl><dd></dd></dl>
<p>where
</p>
<dl><dd></dd></dl>
<p>and
</p>
<dl><dd></dd></dl>
<p>The expectation ranges over different choices of the training set , all sampled from the same joint distribution which can for example be done via <a href="/wiki/Bootstrapping_(statistics)">bootstrapping</a>. 
The three terms represent:
</p>
<p>Since all three terms are non-negative, the irreducible error forms a lower bound on the expected error on unseen samples.<sup><a href="#cite_note-islr-6">[6]</a></sup><sup>: 34 </sup>
</p><p>The more complex the model is, the more data points it will capture, and the lower the bias will be. However, complexity will make the model "move" more to capture the data points, and hence its variance will be larger.
</p>
<h3>Derivation[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=3">edit</a>]</h3>
<p>The derivation of the bias–variance decomposition for squared error proceeds as follows.<sup><a href="#cite_note-8">[8]</a></sup><sup><a href="#cite_note-9">[9]</a></sup> For notational convenience, we abbreviate , and we drop the subscript on our expectation operators. First, recall that, by definition, for any random variable , we have
</p>
<dl><dd></dd></dl>
<p>Rearranging, we get:
</p>
<dl><dd></dd></dl>
<p>Since is <a href="/wiki/Deterministic_algorithm">deterministic</a>, i.e. independent of ,
</p>
<dl><dd></dd></dl>
<p>Thus, given and (because is noise), implies 
</p><p>Also, since 
</p>
<dl><dd></dd></dl>
<p>Thus, since and are independent, we can write
</p>
<dl><dd></dd></dl>
<p>Finally, MSE loss function (or negative log-likelihood) is obtained by taking the expectation value over :
</p>
<dl><dd></dd></dl>
<h2>Approaches[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=4">edit</a>]</h2>
<p><a href="/wiki/Dimensionality_reduction">Dimensionality reduction</a> and <a href="/wiki/Feature_selection">feature selection</a> can decrease variance by simplifying models. Similarly, a larger training set tends to decrease variance. Adding features (predictors) tends to decrease bias, at the expense of introducing additional variance. Learning algorithms typically have some tunable parameters that control bias and variance; for example,
</p>
<ul><li><a href="/wiki/Linear_model">linear</a> and <a href="/wiki/Generalized_linear_model">Generalized linear</a> models can be <a href="/wiki/Regularization_(mathematics)">regularized</a> to decrease their variance at the cost of increasing their bias.<sup><a href="#cite_note-10">[10]</a></sup></li>
<li>In <a href="/wiki/Artificial_neural_network">artificial neural networks</a>, the variance increases and the bias decreases as the number of hidden units increase,<sup><a href="#cite_note-geman-11">[11]</a></sup> although this classical assumption has been the subject of recent debate.<sup><a href="#cite_note-neal2018-4">[4]</a></sup> Like in GLMs, regularization is typically applied.</li>
<li>In <a href="/wiki/K-nearest_neighbor"><i>k</i>-nearest neighbor</a> models, a high value of k leads to high bias and low variance (see below).</li>
<li>In <a href="/wiki/Instance-based_learning">instance-based learning</a>, regularization can be achieved varying the mixture of <a href="/wiki/Prototype">prototypes</a> and exemplars.<sup><a href="#cite_note-12">[12]</a></sup></li>
<li>In <a href="/wiki/Decision_tree">decision trees</a>, the depth of the tree determines the variance. Decision trees are commonly pruned to control variance.<sup><a href="#cite_note-islr-6">[6]</a></sup><sup>: 307 </sup></li></ul>
<p>One way of resolving the trade-off is to use <a href="/wiki/Mixture_models">mixture models</a> and <a href="/wiki/Ensemble_learning">ensemble learning</a>.<sup><a href="#cite_note-13">[13]</a></sup><sup><a href="#cite_note-14">[14]</a></sup> For example, <a href="/wiki/Boosting_(machine_learning)">boosting</a> combines many "weak" (high bias) models in an ensemble that has lower bias than the individual models, while <a href="/wiki/Bootstrap_aggregating">bagging</a> combines "strong" learners in a way that reduces their variance.
</p><p><a href="/wiki/Model_validation">Model validation</a> methods such as <a href="/wiki/Cross-validation_(statistics)">cross-validation (statistics)</a> can be used to tune models so as to optimize the trade-off. 
</p>
<h3><i>k</i>-nearest neighbors[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=5">edit</a>]</h3>
<p>In the case of <a href="/wiki/K-nearest_neighbors_algorithm">k-nearest neighbors regression</a>, when the expectation is taken over the possible labeling of a fixed training set, a <a href="/wiki/Closed-form_expression">closed-form expression</a> exists that relates the bias–variance decomposition to the parameter k:<sup><a href="#cite_note-ESL-7">[7]</a></sup><sup>: 37, 223 </sup>
</p>
<dl><dd></dd></dl>
<p>where are the k nearest neighbors of x in the training set. The bias (first term) is a monotone rising function of k, while the variance (second term) drops off as k is increased. In fact, under "reasonable assumptions" the bias of the first-nearest neighbor (1-NN) estimator vanishes entirely as the size of the training set approaches infinity.<sup><a href="#cite_note-geman-11">[11]</a></sup>
</p>
<h2>Applications[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=6">edit</a>]</h2>
<h3>In regression[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=7">edit</a>]</h3>
<p>The bias–variance decomposition forms the conceptual basis for regression <a href="/wiki/Regularization_(mathematics)">regularization</a> methods such as <a href="/wiki/Lasso_(statistics)">Lasso</a> and <a href="/wiki/Ridge_regression">ridge regression</a>. Regularization methods introduce bias into the regression solution that can reduce variance considerably relative to the <a href="/wiki/Ordinary_least_squares">ordinary least squares (OLS)</a> solution. Although the OLS solution provides non-biased regression estimates, the lower variance solutions produced by regularization techniques provide superior MSE performance.
</p>
<h3>In classification[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=8">edit</a>]</h3>
<p>The bias–variance decomposition was originally formulated for least-squares regression. For the case of <a href="/wiki/Statistical_classification">classification</a> under the <a href="/wiki/0-1_loss">0-1 loss</a> (misclassification rate), it is possible to find a similar decomposition.<sup><a href="#cite_note-15">[15]</a></sup><sup><a href="#cite_note-16">[16]</a></sup> Alternatively, if the classification problem can be phrased as <a href="/wiki/Probabilistic_classification">probabilistic classification</a>, then the expected squared error of the predicted probabilities with respect to the true probabilities can be decomposed as before.<sup><a href="#cite_note-17">[17]</a></sup>
</p><p>It has been argued that as training data increases, the variance of learned models will tend to decrease, and hence that as training data quantity increases, error is minimized by methods that learn models with lesser bias, and that conversely, for smaller training data quantities it is ever more important to minimize variance.<sup><a href="#cite_note-18">[18]</a></sup>
</p>
<h3>In reinforcement learning[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=9">edit</a>]</h3>
<p>Even though the bias–variance decomposition does not directly apply in <a href="/wiki/Reinforcement_learning">reinforcement learning</a>, a similar tradeoff can also characterize generalization. When an agent has limited information on its environment, the suboptimality of an RL algorithm can be decomposed into the sum of two terms: a term related to an asymptotic bias and a term due to overfitting. The asymptotic bias is directly related to the learning algorithm (independently of the quantity of data) while the overfitting term comes from the fact that the amount of data is limited.<sup><a href="#cite_note-19">[19]</a></sup>
</p>
<h3>In human learning[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=10">edit</a>]</h3>
<p>While widely discussed in the context of machine learning, the bias–variance dilemma has been examined in the context of <a href="/wiki/Cognitive_science">human cognition</a>, most notably by <a href="/wiki/Gerd_Gigerenzer">Gerd Gigerenzer</a> and co-workers in the context of learned heuristics. They have argued (see references below) that the human brain resolves the dilemma in the case of the typically sparse, poorly-characterised training-sets provided by experience by adopting high-bias/low variance heuristics. This reflects the fact that a zero-bias approach has poor generalisability to new situations, and also unreasonably presumes precise knowledge of the true state of the world. The resulting heuristics are relatively simple, but produce better inferences in a wider variety of situations.<sup><a href="#cite_note-ReferenceA-20">[20]</a></sup>
</p><p><a href="/wiki/Stuart_Geman">Geman</a> et al.<sup><a href="#cite_note-geman-11">[11]</a></sup> argue that the bias–variance dilemma implies that abilities such as generic <a href="/wiki/Object_recognition">object recognition</a> cannot be learned from scratch, but require a certain degree of "hard wiring" that is later tuned by experience. This is because model-free approaches to inference require impractically large training sets if they are to avoid high variance.
</p>
<h2>See also[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=11">edit</a>]</h2>
<div>
<ul><li><a href="/wiki/Accuracy_and_precision">Accuracy and precision</a></li>
<li><a href="/wiki/Bias_of_an_estimator">Bias of an estimator</a></li>
<li><a href="/wiki/Double_descent">Double descent</a></li>
<li><a href="/wiki/Gauss%E2%80%93Markov_theorem">Gauss–Markov theorem</a></li>
<li><a href="/wiki/Hyperparameter_optimization">Hyperparameter optimization</a></li>
<li><a href="/wiki/Law_of_total_variance">Law of total variance</a></li>
<li><a href="/wiki/Minimum-variance_unbiased_estimator">Minimum-variance unbiased estimator</a></li>
<li><a href="/wiki/Model_selection">Model selection</a></li>
<li><a href="/wiki/Regression_model_validation">Regression model validation</a></li>
<li><a href="/wiki/Supervised_learning">Supervised learning</a></li></ul>
</div>
<h2>References[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=12">edit</a>]</h2>
<div><ol>
<li><b><a href="#cite_ref-1">^</a></b> <cite>Kohavi, Ron; Wolpert, David H. (1996). "Bias Plus Variance Decomposition for Zero-One Loss Functions". <i>ICML</i>. <b>96</b>.</cite>
</li>
<li><b><a href="#cite_ref-2">^</a></b> <cite>Luxburg, Ulrike V.; Schölkopf, B. (2011). "Statistical learning theory: Models, concepts, and results". <i>Handbook of the History of Logic</i>. <b>10</b>: Section 2.4.</cite>
</li>
<li><b><a href="#cite_ref-nealThesis2019_3-0">^</a></b> <cite>Neal, Brady (2019). "On the Bias-Variance Tradeoff: Textbooks Need an Update". <a href="/wiki/ArXiv_(identifier)">arXiv</a>:<a href="//arxiv.org/abs/1912.08286">1912.08286</a> [<a href="//arxiv.org/archive/cs.LG">cs.LG</a>].</cite>
</li>
<li>^ <a href="#cite_ref-neal2018_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-neal2018_4-1"><sup><i><b>b</b></i></sup></a> <cite>Neal, Brady; Mittal, Sarthak; Baratin, Aristide; Tantia, Vinayak; Scicluna, Matthew; Lacoste-Julien, Simon; Mitliagkas, Ioannis (2018). "A Modern Take on the Bias-Variance Tradeoff in Neural Networks". <a href="/wiki/ArXiv_(identifier)">arXiv</a>:<a href="//arxiv.org/abs/1810.08591">1810.08591</a> [<a href="//arxiv.org/archive/cs.LG">cs.LG</a>].</cite>
</li>
<li><b><a href="#cite_ref-5">^</a></b> <cite>Vapnik, Vladimir (2000). <a href="https://dx.doi.org/10.1007/978-1-4757-3264-1"><i>The nature of statistical learning theory</i></a>. New York: Springer-Verlag. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1007%2F978-1-4757-3264-1">10.1007/978-1-4757-3264-1</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4757-3264-1"><bdi>978-1-4757-3264-1</bdi></a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:7138354">7138354</a>.</cite>
</li>
<li>^ <a href="#cite_ref-islr_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-islr_6-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-islr_6-2"><sup><i><b>c</b></i></sup></a> <cite>James, Gareth; <a href="/wiki/Daniela_Witten">Witten, Daniela</a>; <a href="/wiki/Trevor_Hastie">Hastie, Trevor</a>; <a href="/wiki/Robert_Tibshirani">Tibshirani, Robert</a> (2013). <a href="http://www-bcf.usc.edu/~gareth/ISL/"><i>An Introduction to Statistical Learning</i></a>. Springer.</cite>
</li>
<li>^ <a href="#cite_ref-ESL_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ESL_7-1"><sup><i><b>b</b></i></sup></a> <cite>Hastie, Trevor; Tibshirani, Robert; <a href="/wiki/Jerome_H._Friedman">Friedman, Jerome H.</a> (2009). <a href="https://web.archive.org/web/20150126123924/http://statweb.stanford.edu/~tibs/ElemStatLearn/"><i>The Elements of Statistical Learning</i></a>. Archived from <a href="http://statweb.stanford.edu/~tibs/ElemStatLearn/">the original</a> on 2015-01-26. Retrieved 2014-08-20.</cite>
</li>
<li><b><a href="#cite_ref-8">^</a></b> <cite><a href="/wiki/Sethu_Vijayakumar">Vijayakumar, Sethu</a> (2007). <a href="http://www.inf.ed.ac.uk/teaching/courses/mlsc/Notes/Lecture4/BiasVariance.pdf">"The Bias–Variance Tradeoff"</a> (PDF). <a href="/wiki/University_of_Edinburgh">University of Edinburgh</a>. Retrieved 19 August 2014.</cite>
</li>
<li><b><a href="#cite_ref-9">^</a></b> <cite>Shakhnarovich, Greg (2011). <a href="https://web.archive.org/web/20140821063842/http://ttic.uchicago.edu/~gregory/courses/wis-ml2012/lectures/biasVarDecom.pdf">"Notes on derivation of bias-variance decomposition in linear regression"</a> (PDF). Archived from <a href="http://ttic.uchicago.edu/~gregory/courses/wis-ml2012/lectures/biasVarDecom.pdf">the original</a> (PDF) on 21 August 2014. Retrieved 20 August 2014.</cite>
</li>
<li><b><a href="#cite_ref-10">^</a></b> <cite>Belsley, David (1991). <i>Conditioning diagnostics : collinearity and weak data in regression</i>. New York (NY): Wiley. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0471528890"><bdi>978-0471528890</bdi></a>.</cite>
</li>
<li>^ <a href="#cite_ref-geman_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-geman_11-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-geman_11-2"><sup><i><b>c</b></i></sup></a> <cite><a href="/wiki/Stuart_Geman">Geman, Stuart</a>; Bienenstock, Élie; Doursat, René (1992). <a href="http://web.mit.edu/6.435/www/Geman92.pdf">"Neural networks and the bias/variance dilemma"</a> (PDF). <i>Neural Computation</i>. <b>4</b>: 1–58. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1162%2Fneco.1992.4.1.1">10.1162/neco.1992.4.1.1</a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:14215320">14215320</a>.</cite>
</li>
<li><b><a href="#cite_ref-12">^</a></b> <cite>Gagliardi, Francesco (May 2011). <a href="https://www.researchgate.net/publication/51173579">"Instance-based classifiers applied to medical databases: diagnosis and knowledge extraction"</a>. <i>Artificial Intelligence in Medicine</i>. <b>52</b> (3): 123–139. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1016%2Fj.artmed.2011.04.002">10.1016/j.artmed.2011.04.002</a>. <a href="/wiki/PMID_(identifier)">PMID</a> <a href="//pubmed.ncbi.nlm.nih.gov/21621400">21621400</a>.</cite>
</li>
<li><b><a href="#cite_ref-13">^</a></b> <cite>Ting, Jo-Anne; Vijaykumar, Sethu; Schaal, Stefan (2011). "Locally Weighted Regression for Control". In Sammut, Claude; Webb, Geoffrey I. (eds.). <a href="http://homepages.inf.ed.ac.uk/svijayak/publications/ting-EMLDM2016.pdf"><i>Encyclopedia of Machine Learning</i></a> (PDF). Springer. p. 615. <a href="/wiki/Bibcode_(identifier)">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2010eoml.book.....S">2010eoml.book.....S</a>.</cite>
</li>
<li><b><a href="#cite_ref-14">^</a></b> <cite>Fortmann-Roe, Scott (2012). <a href="http://scott.fortmann-roe.com/docs/BiasVariance.html">"Understanding the Bias–Variance Tradeoff"</a>.</cite>
</li>
<li><b><a href="#cite_ref-15">^</a></b> <cite><a href="/wiki/Pedro_Domingos">Domingos, Pedro</a> (2000). <a href="http://homes.cs.washington.edu/~pedrod/bvd.pdf"><i>A unified bias-variance decomposition</i></a> (PDF). ICML.</cite>
</li>
<li><b><a href="#cite_ref-16">^</a></b> <cite>Valentini, Giorgio; <a href="/wiki/Thomas_G._Dietterich">Dietterich, Thomas G.</a> (2004). <a href="http://www.jmlr.org/papers/volume5/valentini04a/valentini04a.pdf">"Bias–variance analysis of support vector machines for the development of SVM-based ensemble methods"</a> (PDF). <i><a href="/wiki/Journal_of_Machine_Learning_Research">Journal of Machine Learning Research</a></i>. <b>5</b>: 725–775.</cite>
</li>
<li><b><a href="#cite_ref-17">^</a></b> <cite>Manning, Christopher D.; Raghavan, Prabhakar; Schütze, Hinrich (2008). <a href="http://nlp.stanford.edu/IR-book/"><i>Introduction to Information Retrieval</i></a>. Cambridge University Press. pp. 308–314.</cite>
</li>
<li><b><a href="#cite_ref-18">^</a></b> <cite>Brain, Damian; <a href="/wiki/Geoff_Webb">Webb, Geoffrey</a> (2002). <a href="http://i.giwebb.com/wp-content/papercite-data/pdf/brainwebb02.pdf"><i>The Need for Low Bias Algorithms in Classification Learning From Large Data Sets</i></a> (PDF). Proceedings of the Sixth European Conference on Principles of Data Mining and Knowledge Discovery (PKDD 2002).</cite>
</li>
<li><b><a href="#cite_ref-19">^</a></b> <cite>Francois-Lavet, Vincent; Rabusseau, Guillaume; Pineau, Joelle; Ernst, Damien; Fonteneau, Raphael (2019). <a href="https://jair.org/index.php/jair/article/view/11478">"On Overfitting and Asymptotic Bias in Batch Reinforcement Learning with Partial Observability"</a>. <i>Journal of AI Research</i>. <b>65</b>: 1–30. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1613%2Fjair.1.11478">10.1613/jair.1.11478</a>.</cite>
</li>
<li><b><a href="#cite_ref-ReferenceA_20-0">^</a></b> <cite><a href="/wiki/Gerd_Gigerenzer">Gigerenzer, Gerd</a>; Brighton, Henry (2009). "Homo Heuristicus: Why Biased Minds Make Better Inferences". <i>Topics in Cognitive Science</i>. <b>1</b> (1): 107–143. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1111%2Fj.1756-8765.2008.01006.x">10.1111/j.1756-8765.2008.01006.x</a>. <a href="/wiki/Hdl_(identifier)">hdl</a>:<a href="//hdl.handle.net/11858%2F00-001M-0000-0024-F678-0">11858/00-001M-0000-0024-F678-0</a>. <a href="/wiki/PMID_(identifier)">PMID</a> <a href="//pubmed.ncbi.nlm.nih.gov/25164802">25164802</a>.</cite>
</li>
</ol></div>
<h2>External links[<a href="/w/index.php?title=Bias%E2%80%93variance_tradeoff&amp;action=edit&amp;section=13">edit</a>]</h2>
<ul><li><a href="https://mlu-explain.github.io/bias-variance/">MLU-Explain: The Bias Variance Tradeoff</a> — An interactive visualization of the bias-variance tradeoff in LOESS Regression and K-Nearest Neighbors.</li></ul>
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 Contents

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 * (Top)
 * 1 Motivation
 * 2 Bias–variance decomposition of mean squared error
 + 2.1 Derivation
 * 3 Approaches
 + 3.1 k-nearest neighbors
 * 4 Applications
 + 4.1 In regression
 + 4.2 In classification
 + 4.3 In reinforcement learning
 + 4.4 In human learning
 * 5 See also
 * 6 References
 * 7 External links
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 Bias–variance tradeoff

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 From Wikipedia, the free encyclopedia
 Part of a series on 
 Machine learning 
 and data mining 
  
 Paradigms 
 * Supervised learning 
 * Unsupervised learning 
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 ( classification • regression ) 
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 + Bagging 
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 Function and noisy data
 Spread=5
 Spread=1
 Spread=0.1
 A function (red) is approximated using radial basis functions (blue). Several trials are shown in each graph. For each trial, a few noisy data points are provided as a training set (top). For a wide spread (image 2) the bias is high: the RBFs cannot fully approximate the function (especially the central dip), but the variance between different trials is low. As spread decreases (image 3 and 4) the bias decreases: the blue curves more closely approximate the red. However, depending on the noise in different trials the variance between trials increases. In the lowermost image the approximated values for x=0 varies wildly depending on where the data points were located.
 Bias and variance as function of model complexity

 In statistics and machine learning, the bias–variance tradeoff is the property of a model that the variance of the parameter estimated across samples can be reduced by increasing the bias in the estimated parameters. The bias–variance dilemma or bias–variance problem is the conflict in trying to simultaneously minimize these two sources of error that prevent supervised learning algorithms from generalizing beyond their training set:[1][2]

 * The bias error is an error from erroneous assumptions in the learning algorithm. High bias can cause an algorithm to miss the relevant relations between features and target outputs (underfitting).
 * The variance is an error from sensitivity to small fluctuations in the training set. High variance may result from an algorithm modeling the random noise in the training data (overfitting).

 The bias–variance decomposition is a way of analyzing a learning algorithm's expected generalization error with respect to a particular problem as a sum of three terms, the bias, variance, and a quantity called the irreducible error, resulting from noise in the problem itself.

 Motivation [ edit ]

 * bias low, variance low

 * bias high,
 variance low

 * bias low,
 variance high

 * bias high,
 variance high

 The bias–variance tradeoff is a central problem in supervised learning. Ideally, one wants to choose a model that both accurately captures the regularities in its training data, but also generalizes well to unseen data. Unfortunately, it is typically impossible to do both simultaneously. High-variance learning methods may be able to represent their training set well but are at risk of overfitting to noisy or unrepresentative training data. In contrast, algorithms with high bias typically produce simpler models that may fail to capture important regularities (i.e. underfit) in the data.

 It is an often made fallacy[3][4] to assume that complex models must have high variance; High variance models are 'complex' in some sense, but the reverse needs not be true[ clarification needed ]. In addition, one has to be careful how to define complexity: In particular, the number of parameters used to describe the model is a poor measure of complexity. This is illustrated by an example adapted from:[5] The model has only two parameters () but it can interpolate any number of points by oscillating with a high enough frequency, resulting in both a high bias and high variance.

 An analogy can be made to the relationship between accuracy and precision. Accuracy is a description of bias and can intuitively be improved by selecting from only local information. Consequently, a sample will appear accurate (i.e. have low bias) under the aforementioned selection conditions, but may result in underfitting. In other words, test data may not agree as closely with training data, which would indicate imprecision and therefore inflated variance. A graphical example would be a straight line fit to data exhibiting quadratic behavior overall. Precision is a description of variance and generally can only be improved by selecting information from a comparatively larger space. The option to select many data points over a broad sample space is the ideal condition for any analysis. However, intrinsic constraints (whether physical, theoretical, computational, etc.) will always play a limiting role. The limiting case where only a finite number of data points are selected over a broad sample space may result in improved precision and lower variance overall, but may also result in an overreliance on the training data (overfitting). This means that test data would also not agree as closely with the training data, but in this case the reason is due to inaccuracy or high bias. To borrow from the previous example, the graphical representation would appear as a high-order polynomial fit to the same data exhibiting quadratic behavior. Note that error in each case is measured the same way, but the reason ascribed to the error is different depending on the balance between bias and variance. To mitigate how much information is used from neighboring observations, a model can be smoothed via explicit regularization, such as shrinkage.

 Bias–variance decomposition of mean squared error [ edit ]

 Main article: Mean squared error

 Suppose that we have a training set consisting of a set of points and real values associated with each point . We assume that there is a function f(x) such as , where the noise, , has zero mean and variance .

 We want to find a function , that approximates the true function as well as possible, by means of some learning algorithm based on a training dataset (sample) . We make "as well as possible" precise by measuring the mean squared error between and : we want to be minimal, both for and for points outside of our sample. Of course, we cannot hope to do so perfectly, since the contain noise ; this means we must be prepared to accept an irreducible error in any function we come up with.

 Finding an that generalizes to points outside of the training set can be done with any of the countless algorithms used for supervised learning. It turns out that whichever function we select, we can decompose its expected error on an unseen sample as follows:[6] : 34 [7] : 223

 where

 and

 The expectation ranges over different choices of the training set , all sampled from the same joint distribution which can for example be done via bootstrapping. The three terms represent:

 * the square of the bias of the learning method, which can be thought of as the error caused by the simplifying assumptions built into the method. E.g., when approximating a non-linear function using a learning method for linear models, there will be error in the estimates due to this assumption;
 * the variance of the learning method, or, intuitively, how much the learning method will move around its mean;
 * the irreducible error .

 Since all three terms are non-negative, the irreducible error forms a lower bound on the expected error on unseen samples.[6] : 34

 The more complex the model is, the more data points it will capture, and the lower the bias will be. However, complexity will make the model "move" more to capture the data points, and hence its variance will be larger.

 Derivation [ edit ]

 The derivation of the bias–variance decomposition for squared error proceeds as follows.[8][9] For notational convenience, we abbreviate , and we drop the subscript on our expectation operators. First, recall that, by definition, for any random variable , we have

 Rearranging, we get:

 Since is deterministic, i.e. independent of ,

 Thus, given and (because is noise), implies

 Also, since

 Thus, since and are independent, we can write

 Finally, MSE loss function (or negative log-likelihood) is obtained by taking the expectation value over :

 Approaches [ edit ]

 Dimensionality reduction and feature selection can decrease variance by simplifying models. Similarly, a larger training set tends to decrease variance. Adding features (predictors) tends to decrease bias, at the expense of introducing additional variance. Learning algorithms typically have some tunable parameters that control bias and variance; for example,

 * linear and Generalized linear models can be regularized to decrease their variance at the cost of increasing their bias.[10]
 * In artificial neural networks, the variance increases and the bias decreases as the number of hidden units increase,[11] although this classical assumption has been the subject of recent debate.[4] Like in GLMs, regularization is typically applied.
 * In k-nearest neighbor models, a high value of k leads to high bias and low variance (see below).
 * In instance-based learning, regularization can be achieved varying the mixture of prototypes and exemplars.[12]
 * In decision trees, the depth of the tree determines the variance. Decision trees are commonly pruned to control variance.[6] : 307

 One way of resolving the trade-off is to use mixture models and ensemble learning.[13][14] For example, boosting combines many "weak" (high bias) models in an ensemble that has lower bias than the individual models, while bagging combines "strong" learners in a way that reduces their variance.

 Model validation methods such as cross-validation (statistics) can be used to tune models so as to optimize the trade-off.

 k -nearest neighbors [ edit ]

 In the case of k -nearest neighbors regression, when the expectation is taken over the possible labeling of a fixed training set, a closed-form expression exists that relates the bias–variance decomposition to the parameter k :[7] : 37, 223

 where are the k nearest neighbors of x in the training set. The bias (first term) is a monotone rising function of k , while the variance (second term) drops off as k is increased. In fact, under "reasonable assumptions" the bias of the first-nearest neighbor (1-NN) estimator vanishes entirely as the size of the training set approaches infinity.[11]

 Applications [ edit ]

 In regression [ edit ]

 The bias–variance decomposition forms the conceptual basis for regression regularization methods such as Lasso and ridge regression. Regularization methods introduce bias into the regression solution that can reduce variance considerably relative to the ordinary least squares (OLS) solution. Although the OLS solution provides non-biased regression estimates, the lower variance solutions produced by regularization techniques provide superior MSE performance.

 In classification [ edit ]

 The bias–variance decomposition was originally formulated for least-squares regression. For the case of classification under the 0-1 loss (misclassification rate), it is possible to find a similar decomposition.[15][16] Alternatively, if the classification problem can be phrased as probabilistic classification, then the expected squared error of the predicted probabilities with respect to the true probabilities can be decomposed as before.[17]

 It has been argued that as training data increases, the variance of learned models will tend to decrease, and hence that as training data quantity increases, error is minimized by methods that learn models with lesser bias, and that conversely, for smaller training data quantities it is ever more important to minimize variance.[18]

 In reinforcement learning [ edit ]

 Even though the bias–variance decomposition does not directly apply in reinforcement learning, a similar tradeoff can also characterize generalization. When an agent has limited information on its environment, the suboptimality of an RL algorithm can be decomposed into the sum of two terms: a term related to an asymptotic bias and a term due to overfitting. The asymptotic bias is directly related to the learning algorithm (independently of the quantity of data) while the overfitting term comes from the fact that the amount of data is limited.[19]

 In human learning [ edit ]

 While widely discussed in the context of machine learning, the bias–variance dilemma has been examined in the context of human cognition, most notably by Gerd Gigerenzer and co-workers in the context of learned heuristics. They have argued (see references below) that the human brain resolves the dilemma in the case of the typically sparse, poorly-characterised training-sets provided by experience by adopting high-bias/low variance heuristics. This reflects the fact that a zero-bias approach has poor generalisability to new situations, and also unreasonably presumes precise knowledge of the true state of the world. The resulting heuristics are relatively simple, but produce better inferences in a wider variety of situations.[20]

 Geman et al.[11] argue that the bias–variance dilemma implies that abilities such as generic object recognition cannot be learned from scratch, but require a certain degree of "hard wiring" that is later tuned by experience. This is because model-free approaches to inference require impractically large training sets if they are to avoid high variance.

 See also [ edit ]

 * Accuracy and precision
 * Bias of an estimator
 * Double descent
 * Gauss–Markov theorem
 * Hyperparameter optimization
 * Law of total variance
 * Minimum-variance unbiased estimator
 * Model selection
 * Regression model validation
 * Supervised learning

 References [ edit ]

 1. ^ Kohavi, Ron; Wolpert, David H. (1996). "Bias Plus Variance Decomposition for Zero-One Loss Functions". ICML. 96.
 2. ^ Luxburg, Ulrike V.; Schölkopf, B. (2011). "Statistical learning theory: Models, concepts, and results". Handbook of the History of Logic. 10: Section 2.4.
 3. ^ Neal, Brady (2019). "On the Bias-Variance Tradeoff: Textbooks Need an Update". arXiv:1912.08286 [cs.LG].
 4. ^ a b Neal, Brady; Mittal, Sarthak; Baratin, Aristide; Tantia, Vinayak; Scicluna, Matthew; Lacoste-Julien, Simon; Mitliagkas, Ioannis (2018). "A Modern Take on the Bias-Variance Tradeoff in Neural Networks". arXiv:1810.08591 [cs.LG].
 5. ^ Vapnik, Vladimir (2000). The nature of statistical learning theory. New York: Springer-Verlag. doi:10.1007/978-1-4757-3264-1. ISBN 978-1-4757-3264-1. S2CID 7138354.
 6. ^ a b c James, Gareth; Witten, Daniela; Hastie, Trevor; Tibshirani, Robert (2013). An Introduction to Statistical Learning. Springer.
 7. ^ a b Hastie, Trevor; Tibshirani, Robert; Friedman, Jerome H. (2009). The Elements of Statistical Learning. Archived from the original on 2015-01-26 . Retrieved 2014-08-20 .
 8. ^ Vijayakumar, Sethu (2007). "The Bias–Variance Tradeoff" (PDF) . University of Edinburgh . Retrieved 19 August 2014 .
 9. ^ Shakhnarovich, Greg (2011). "Notes on derivation of bias-variance decomposition in linear regression" (PDF) . Archived from the original (PDF) on 21 August 2014 . Retrieved 20 August 2014 .
 10. ^ Belsley, David (1991). Conditioning diagnostics : collinearity and weak data in regression. New York (NY): Wiley. ISBN 978-0471528890.
 11. ^ a b c Geman, Stuart; Bienenstock, Élie; Doursat, René (1992). "Neural networks and the bias/variance dilemma" (PDF) . Neural Computation. 4: 1–58. doi:10.1162/neco.1992.4.1.1. S2CID 14215320.
 12. ^ Gagliardi, Francesco (May 2011). "Instance-based classifiers applied to medical databases: diagnosis and knowledge extraction". Artificial Intelligence in Medicine. 52 (3): 123–139. doi:10.1016/j.artmed.2011.04.002. PMID 21621400.
 13. ^ Ting, Jo-Anne; Vijaykumar, Sethu; Schaal, Stefan (2011). "Locally Weighted Regression for Control". In Sammut, Claude; Webb, Geoffrey I. (eds.). Encyclopedia of Machine Learning (PDF) . Springer. p. 615. Bibcode:2010eoml.book.....S.
 14. ^ Fortmann-Roe, Scott (2012). "Understanding the Bias–Variance Tradeoff".
 15. ^ Domingos, Pedro (2000). A unified bias-variance decomposition (PDF) . ICML.
 16. ^ Valentini, Giorgio; Dietterich, Thomas G. (2004). "Bias–variance analysis of support vector machines for the development of SVM-based ensemble methods" (PDF) . Journal of Machine Learning Research. 5: 725–775.
 17. ^ Manning, Christopher D.; Raghavan, Prabhakar; Schütze, Hinrich (2008). Introduction to Information Retrieval. Cambridge University Press. pp. 308–314.
 18. ^ Brain, Damian; Webb, Geoffrey (2002). The Need for Low Bias Algorithms in Classification Learning From Large Data Sets (PDF) . Proceedings of the Sixth European Conference on Principles of Data Mining and Knowledge Discovery (PKDD 2002).
 19. ^ Francois-Lavet, Vincent; Rabusseau, Guillaume; Pineau, Joelle; Ernst, Damien; Fonteneau, Raphael (2019). "On Overfitting and Asymptotic Bias in Batch Reinforcement Learning with Partial Observability". Journal of AI Research. 65: 1–30. doi:10.1613/jair.1.11478.
 20. ^ Gigerenzer, Gerd; Brighton, Henry (2009). "Homo Heuristicus: Why Biased Minds Make Better Inferences". Topics in Cognitive Science. 1 (1): 107–143. doi:10.1111/j.1756-8765.2008.01006.x. hdl:11858/00-001M-0000-0024-F678-0. PMID 25164802.

 External links [ edit ]

 * MLU-Explain: The Bias Variance Tradeoff — An interactive visualization of the bias-variance tradeoff in LOESS Regression and K-Nearest Neighbors.
 Retrieved from "https://en.wikipedia.org/w/index.php?title=Bias–variance_tradeoff&oldid=1135963813"
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From Wikipedia, the free encyclopedia
	 
      Function and noisy data       Spread=5       Spread=1       Spread=0.1   A function (red) is approximated using radial basis functions (blue). Several trials are shown in each graph. For each trial, a few noisy data points are provided as a training set (top). For a wide spread (image 2) the bias is high: the RBFs cannot fully approximate the function (especially the central dip), but the variance between different trials is low. As spread decreases (image 3 and 4) the bias decreases: the blue curves more closely approximate the red. However, depending on the noise in different trials the variance between trials increases. In the lowermost image the approximated values for x=0 varies wildly depending on where the data points were located.  
      Bias and variance as function of model complexity  
In statistics and machine learning, the bias–variance tradeoff is the property of a model that the variance of the parameter estimated across samples can be reduced by increasing the bias in the estimated parameters.
The bias–variance dilemma or bias–variance problem is the conflict in trying to simultaneously minimize these two sources of error that prevent supervised learning algorithms from generalizing beyond their training set: [1]   [2] 
 The  bias  error is an error from erroneous assumptions in the learning algorithm. High bias can cause an algorithm to miss the relevant relations between features and target outputs (underfitting).
The  variance  is an error from sensitivity to small fluctuations in the training set. High variance may result from an algorithm modeling the random noise in the training data (overfitting). 
The bias–variance decomposition is a way of analyzing a learning algorithm's expected generalization error with respect to a particular problem as a sum of three terms, the bias, variance, and a quantity called the irreducible error, resulting from noise in the problem itself.
Motivation[edit]
	 
	     
	bias low, variance low
	 
	 
	     
	bias high,variance low
	 
	 
	     
	bias low,variance high
	 
	 
	     
	bias high,variance high
	 
The bias–variance tradeoff is a central problem in supervised learning. Ideally, one wants to choose a model that both accurately captures the regularities in its training data, but also generalizes well to unseen data. Unfortunately, it is typically impossible to do both simultaneously. High-variance learning methods may be able to represent their training set well but are at risk of overfitting to noisy or unrepresentative training data. In contrast, algorithms with high bias typically produce simpler models that may fail to capture important regularities (i.e. underfit) in the data.
 It is an often made fallacy  [3]   [4]  to assume that complex models must have high variance; High variance models are 'complex' in some sense, but the reverse needs not be true[ clarification needed ].
In addition, one has to be careful how to define complexity: In particular, the number of parameters used to describe the model is a poor measure of complexity. This is illustrated by an example adapted from: [5]  The model has only two parameters () but it can interpolate any number of points by oscillating with a high enough frequency, resulting in both a high bias and high variance.
 An analogy can be made to the relationship between accuracy and precision. Accuracy is a description of bias and can intuitively be improved by selecting from only local information. Consequently, a sample will appear accurate (i.e. have low bias) under the aforementioned selection conditions, but may result in underfitting. In other words, test data may not agree as closely with training data, which would indicate imprecision and therefore inflated variance. A graphical example would be a straight line fit to data exhibiting quadratic behavior overall. Precision is a description of variance and generally can only be improved by selecting information from a comparatively larger space. The option to select many data points over a broad sample space is the ideal condition for any analysis. However, intrinsic constraints (whether physical, theoretical, computational, etc.) will always play a limiting role. The limiting case where only a finite number of data points are selected over a broad sample space may result in improved precision and lower variance overall, but may also result in an overreliance on the training data (overfitting). This means that test data would also not agree as closely with the training data, but in this case the reason is due to inaccuracy or high bias. To borrow from the previous example, the graphical representation would appear as a high-order polynomial fit to the same data exhibiting quadratic behavior. Note that error in each case is measured the same way, but the reason ascribed to the error is different depending on the balance between bias and variance. To mitigate how much information is used from neighboring observations, a model can be smoothed via explicit regularization, such as shrinkage.
Bias–variance decomposition of mean squared error[edit]
Suppose that we have a training set consisting of a set of points and real values associated with each point . We assume that there is a function f(x) such as , where the noise, , has zero mean and variance .
 We want to find a function , that approximates the true function as well as possible, by means of some learning algorithm based on a training dataset (sample) . We make "as well as possible" precise by measuring the mean squared error between and : we want to be minimal, both for and for points outside of our sample. Of course, we cannot hope to do so perfectly, since the contain noise ; this means we must be prepared to accept an irreducible error in any function we come up with.
 Finding an that generalizes to points outside of the training set can be done with any of the countless algorithms used for supervised learning. It turns out that whichever function we select, we can decompose its expected error on an unseen sample as follows: [6]  : 34   [7]  : 223 
   
where
   
and
   
The expectation ranges over different choices of the training set , all sampled from the same joint distribution which can for example be done via bootstrapping. 
The three terms represent:
Since all three terms are non-negative, the irreducible error forms a lower bound on the expected error on unseen samples. [6]  : 34 
 The more complex the model is, the more data points it will capture, and the lower the bias will be. However, complexity will make the model "move" more to capture the data points, and hence its variance will be larger.
Derivation[edit]
The derivation of the bias–variance decomposition for squared error proceeds as follows. [8]   [9]  For notational convenience, we abbreviate , and we drop the subscript on our expectation operators. First, recall that, by definition, for any random variable , we have
   
Rearranging, we get:
   
Since is deterministic, i.e. independent of ,
   
Thus, given and (because is noise), implies 
 Also, since 
   
Thus, since and are independent, we can write
   
Finally, MSE loss function (or negative log-likelihood) is obtained by taking the expectation value over :
   
Approaches[edit]
 Dimensionality reduction and feature selection can decrease variance by simplifying models. Similarly, a larger training set tends to decrease variance. Adding features (predictors) tends to decrease bias, at the expense of introducing additional variance. Learning algorithms typically have some tunable parameters that control bias and variance; for example,
  linear and Generalized linear models can be regularized to decrease their variance at the cost of increasing their bias. [10]  
In artificial neural networks, the variance increases and the bias decreases as the number of hidden units increase, [11]  although this classical assumption has been the subject of recent debate. [4]  Like in GLMs, regularization is typically applied.
In  k-nearest neighbor models, a high value of k leads to high bias and low variance (see below).
In instance-based learning, regularization can be achieved varying the mixture of prototypes and exemplars. [12]  
In decision trees, the depth of the tree determines the variance. Decision trees are commonly pruned to control variance. [6]  : 307   
One way of resolving the trade-off is to use mixture models and ensemble learning. [13]   [14]  For example, boosting combines many "weak" (high bias) models in an ensemble that has lower bias than the individual models, while bagging combines "strong" learners in a way that reduces their variance.
  Model validation methods such as cross-validation (statistics) can be used to tune models so as to optimize the trade-off. 
 k-nearest neighbors[edit]
In the case of k-nearest neighbors regression, when the expectation is taken over the possible labeling of a fixed training set, a closed-form expression exists that relates the bias–variance decomposition to the parameter k: [7]  : 37, 223 
   
where are the k nearest neighbors of x in the training set. The bias (first term) is a monotone rising function of k, while the variance (second term) drops off as k is increased. In fact, under "reasonable assumptions" the bias of the first-nearest neighbor (1-NN) estimator vanishes entirely as the size of the training set approaches infinity. [11] 
Applications[edit]
In regression[edit]
The bias–variance decomposition forms the conceptual basis for regression regularization methods such as Lasso and ridge regression. Regularization methods introduce bias into the regression solution that can reduce variance considerably relative to the ordinary least squares (OLS) solution. Although the OLS solution provides non-biased regression estimates, the lower variance solutions produced by regularization techniques provide superior MSE performance.
In classification[edit]
The bias–variance decomposition was originally formulated for least-squares regression. For the case of classification under the 0-1 loss (misclassification rate), it is possible to find a similar decomposition. [15]   [16]  Alternatively, if the classification problem can be phrased as probabilistic classification, then the expected squared error of the predicted probabilities with respect to the true probabilities can be decomposed as before. [17] 
 It has been argued that as training data increases, the variance of learned models will tend to decrease, and hence that as training data quantity increases, error is minimized by methods that learn models with lesser bias, and that conversely, for smaller training data quantities it is ever more important to minimize variance. [18] 
In reinforcement learning[edit]
Even though the bias–variance decomposition does not directly apply in reinforcement learning, a similar tradeoff can also characterize generalization. When an agent has limited information on its environment, the suboptimality of an RL algorithm can be decomposed into the sum of two terms: a term related to an asymptotic bias and a term due to overfitting. The asymptotic bias is directly related to the learning algorithm (independently of the quantity of data) while the overfitting term comes from the fact that the amount of data is limited. [19] 
In human learning[edit]
While widely discussed in the context of machine learning, the bias–variance dilemma has been examined in the context of human cognition, most notably by Gerd Gigerenzer and co-workers in the context of learned heuristics. They have argued (see references below) that the human brain resolves the dilemma in the case of the typically sparse, poorly-characterised training-sets provided by experience by adopting high-bias/low variance heuristics. This reflects the fact that a zero-bias approach has poor generalisability to new situations, and also unreasonably presumes precise knowledge of the true state of the world. The resulting heuristics are relatively simple, but produce better inferences in a wider variety of situations. [20] 
  Geman et al. [11]  argue that the bias–variance dilemma implies that abilities such as generic object recognition cannot be learned from scratch, but require a certain degree of "hard wiring" that is later tuned by experience. This is because model-free approaches to inference require impractically large training sets if they are to avoid high variance.
See also[edit]
  Accuracy and precision 
 Bias of an estimator 
 Double descent 
 Gauss–Markov theorem 
 Hyperparameter optimization 
 Law of total variance 
 Minimum-variance unbiased estimator 
 Model selection 
 Regression model validation 
 Supervised learning  
References[edit]
 
  ^  Kohavi, Ron; Wolpert, David H. (1996). "Bias Plus Variance Decomposition for Zero-One Loss Functions". ICML. 96.
  ^  Luxburg, Ulrike V.; Schölkopf, B. (2011). "Statistical learning theory: Models, concepts, and results". Handbook of the History of Logic. 10: Section 2.4.
  ^  Neal, Brady (2019). "On the Bias-Variance Tradeoff: Textbooks Need an Update". arXiv:1912.08286 [cs.LG].
^    a       b    Neal, Brady; Mittal, Sarthak; Baratin, Aristide; Tantia, Vinayak; Scicluna, Matthew; Lacoste-Julien, Simon; Mitliagkas, Ioannis (2018). "A Modern Take on the Bias-Variance Tradeoff in Neural Networks". arXiv:1810.08591 [cs.LG].
  ^  Vapnik, Vladimir (2000).  The nature of statistical learning theory . New York: Springer-Verlag. doi:10.1007/978-1-4757-3264-1. ISBN  978-1-4757-3264-1 . S2CID 7138354.
^    a       b       c    James, Gareth; Witten, Daniela; Hastie, Trevor; Tibshirani, Robert (2013).  An Introduction to Statistical Learning . Springer.
^    a       b    Hastie, Trevor; Tibshirani, Robert; Friedman, Jerome H. (2009).  The Elements of Statistical Learning . Archived from the original on 2015-01-26. Retrieved 2014-08-20.
  ^   Vijayakumar, Sethu (2007). "The Bias–Variance Tradeoff" (PDF). University of Edinburgh. Retrieved 19 August 2014.
  ^  Shakhnarovich, Greg (2011). "Notes on derivation of bias-variance decomposition in linear regression" (PDF). Archived from the original (PDF) on 21 August 2014. Retrieved 20 August 2014.
  ^  Belsley, David (1991). Conditioning diagnostics : collinearity and weak data in regression. New York (NY): Wiley. ISBN  978-0471528890 .
^    a       b       c     Geman, Stuart; Bienenstock, Élie; Doursat, René (1992). "Neural networks and the bias/variance dilemma" (PDF). Neural Computation. 4: 1–58. doi:10.1162/neco.1992.4.1.1. S2CID 14215320.
  ^  Gagliardi, Francesco (May 2011). "Instance-based classifiers applied to medical databases: diagnosis and knowledge extraction". Artificial Intelligence in Medicine. 52 (3): 123–139. doi:10.1016/j.artmed.2011.04.002. PMID 21621400.
  ^  Ting, Jo-Anne; Vijaykumar, Sethu; Schaal, Stefan (2011). "Locally Weighted Regression for Control". In Sammut, Claude; Webb, Geoffrey I. (eds.).  Encyclopedia of Machine Learning  (PDF). Springer. p. 615. Bibcode:2010eoml.book.....S.
  ^  Fortmann-Roe, Scott (2012). "Understanding the Bias–Variance Tradeoff".
  ^   Domingos, Pedro (2000).  A unified bias-variance decomposition  (PDF). ICML.
  ^  Valentini, Giorgio; Dietterich, Thomas G. (2004). "Bias–variance analysis of support vector machines for the development of SVM-based ensemble methods" (PDF).  Journal of Machine Learning Research . 5: 725–775.
  ^  Manning, Christopher D.; Raghavan, Prabhakar; Schütze, Hinrich (2008).  Introduction to Information Retrieval . Cambridge University Press. pp. 308–314.
  ^  Brain, Damian; Webb, Geoffrey (2002).  The Need for Low Bias Algorithms in Classification Learning From Large Data Sets  (PDF). Proceedings of the Sixth European Conference on Principles of Data Mining and Knowledge Discovery (PKDD 2002).
  ^  Francois-Lavet, Vincent; Rabusseau, Guillaume; Pineau, Joelle; Ernst, Damien; Fonteneau, Raphael (2019). "On Overfitting and Asymptotic Bias in Batch Reinforcement Learning with Partial Observability". Journal of AI Research. 65: 1–30. doi:10.1613/jair.1.11478.
  ^   Gigerenzer, Gerd; Brighton, Henry (2009). "Homo Heuristicus: Why Biased Minds Make Better Inferences". Topics in Cognitive Science. 1 (1): 107–143. doi:10.1111/j.1756-8765.2008.01006.x. hdl:11858/00-001M-0000-0024-F678-0. PMID 25164802.
 
External links[edit]
  MLU-Explain: The Bias Variance Tradeoff — An interactive visualization of the bias-variance tradeoff in LOESS Regression and K-Nearest Neighbors.
Bias–variance tradeoff - Wikipedia
https://en.wikipedia.org/wiki/Bias%E2%80%93variance_tradeoff
https://en.wikipedia.org/wiki/Overfitting
Overfitting - Wikipedia
2003-01-23
None
<div><div>
	<p>From Wikipedia, the free encyclopedia</p>
	</div><div>
<div><p><a href="/wiki/File:Overfitting.svg"></a></p><div><p>Figure 1.  The green line represents an overfitted model and the black line represents a regularized model. While the green line best follows the training data, it is too dependent on that data and it is likely to have a higher error rate on new unseen data, compared to the black line.</p></div></div>
<div><p><a href="/wiki/File:Overfitted_Data.png"></a></p><div><p>Figure 2.  Noisy (roughly linear) data is fitted to a linear function and a <a href="/wiki/Polynomial">polynomial</a> function. Although the polynomial function is a perfect fit, the linear function can be expected to generalize better: if the two functions were used to extrapolate beyond the fitted data, the linear function should make better predictions.</p></div></div>
<div><p><a href="/wiki/File:Parabola_on_line.png"></a></p><div><p>Figure 3.  The blue dashed line represents an underfitted model. A straight line can never fit a parabola. This model is too simple.</p></div></div>
<p>In mathematical modeling, <b>overfitting</b> is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably".<sup><a href="#cite_note-1">[1]</a></sup> An <b>overfitted model</b> is a <a href="/wiki/Mathematical_model">mathematical model</a> that contains more <a href="/wiki/Parameter">parameters</a> than can be justified by the data.<sup><a href="#cite_note-CDS-2">[2]</a></sup> The essence of overfitting is to have unknowingly extracted some of the residual variation (i.e., the <a href="/wiki/Statistical_noise">noise</a>) as if that variation represented underlying model structure.<sup><a href="#cite_note-BA2002-3">[3]</a></sup><sup>: 45 </sup>
</p><p><b>Underfitting</b> occurs when a mathematical model cannot adequately capture the underlying structure of the data. An <b>under-fitted model</b> is a model where some parameters or terms that would appear in a correctly specified model are missing.<sup><a href="#cite_note-CDS-2">[2]</a></sup> Under-fitting would occur, for example, when fitting a linear model to non-linear data. Such a model will tend to have poor predictive performance.
</p><p>The possibility of over-fitting exists because the criterion used for <a href="/wiki/Model_selection">selecting the model</a> is not the same as the criterion used to judge the suitability of a model. For example, a model might be selected by maximizing its performance on some set of <a href="/wiki/Training_data">training data</a>, and yet its suitability might be determined by its ability to perform well on unseen data; then over-fitting occurs when a model begins to "memorize" training data rather than "learning" to generalize from a trend. 
</p><p>As an extreme example, if the number of parameters is the same as or greater than the number of observations, then a model can perfectly predict the training data simply by memorizing the data in its entirety. (For an illustration, see Figure 2.) Such a model, though, will typically fail severely when making predictions. 
</p><p>The potential for overfitting depends not only on the number of parameters and data but also the conformability of the model structure with the data shape, and the magnitude of model error compared to the expected level of noise or error in the data.<sup>[<i><a href="/wiki/Wikipedia:Citation_needed">citation needed</a></i>]</sup> Even when the fitted model does not have an excessive number of parameters, it is to be expected that the fitted relationship will appear to perform less well on a new data set than on the data set used for fitting (a phenomenon sometimes known as <i>shrinkage</i>).<sup><a href="#cite_note-CDS-2">[2]</a></sup> In particular, the value of the <a href="/wiki/Coefficient_of_determination">coefficient of determination</a> will <a href="/wiki/Shrinkage_(statistics)">shrink</a> relative to the original data.
</p><p>To lessen the chance or amount of overfitting, several techniques are available (e.g., <a href="/wiki/Model_selection">model comparison</a>, <a href="/wiki/Cross-validation_(statistics)">cross-validation</a>, <a href="/wiki/Regularization_(mathematics)">regularization</a>, <a href="/wiki/Early_stopping">early stopping</a>, <a href="/wiki/Pruning_(algorithm)">pruning</a>, <a href="/wiki/Prior_distribution">Bayesian priors</a>, or <a href="/wiki/Dropout_(neural_networks)">dropout</a>). The basis of some techniques is either (1) to explicitly penalize overly complex models or (2) to test the model's ability to generalize by evaluating its performance on a set of data not used for training, which is assumed to approximate the typical unseen data that a model will encounter.
</p>
<h2>Statistical inference[<a href="/w/index.php?title=Overfitting&amp;action=edit&amp;section=1">edit</a>]</h2>
<table><tbody><tr><td><a href="/wiki/File:Wiki_letter_w_cropped.svg"></a></td><td><p>This section <b>needs expansion</b>. You can help by <a href="https://en.wikipedia.org/w/index.php?title=Overfitting&amp;action=edit&amp;section=">adding to it</a>. <i>(October 2017)</i></p></td></tr></tbody></table>
<p>In statistics, an <a href="/wiki/Statistical_inference">inference</a> is drawn from a <a href="/wiki/Statistical_model">statistical model</a>, which has been <a href="/wiki/Model_selection">selected</a> via some procedure. Burnham &amp; Anderson, in their much-cited text on model selection, argue that to avoid overfitting, we should adhere to the "<a href="/wiki/Principle_of_Parsimony">Principle of Parsimony</a>".<sup><a href="#cite_note-BA2002-3">[3]</a></sup> The authors also state the following.<sup><a href="#cite_note-BA2002-3">[3]</a></sup><sup>: 32–33 </sup>
</p>
<blockquote><p>Overfitted models … are often free of bias in the parameter estimators, but have estimated (and actual) sampling variances that are needlessly large (the precision of the estimators is poor, relative to what could have been accomplished with a more parsimonious model). False treatment effects tend to be identified, and false variables are included with overfitted models. … A best approximating model is achieved by properly balancing the errors of underfitting and overfitting.</p></blockquote>
<p>Overfitting is more likely to be a serious concern when there is little theory available to guide the analysis, in part because then there tend to be a large number of models to select from. The book <i>Model Selection and Model Averaging</i> (2008) puts it this way.<sup><a href="#cite_note-4">[4]</a></sup>
</p>
<blockquote><p>Given a data set, you can fit thousands of models at the push of a button, but how do you choose the best? With so many candidate models, overfitting is a real danger. Is the <a href="/wiki/Infinite_monkey_theorem">monkey who typed Hamlet</a> actually a good writer?</p></blockquote>
<h3>Regression[<a href="/w/index.php?title=Overfitting&amp;action=edit&amp;section=2">edit</a>]</h3>
<p>In <a href="/wiki/Regression_analysis">regression analysis</a>, overfitting occurs frequently.<sup><a href="#cite_note-RMS-5">[5]</a></sup> As an extreme example, if there are <i>p</i> variables in a <a href="/wiki/Linear_regression">linear regression</a> with <i>p</i> data points, the fitted line can go exactly through every point.<sup><a href="#cite_note-6">[6]</a></sup> For <a href="/wiki/Logistic_regression">logistic regression</a> or Cox <a href="/wiki/Proportional_hazards_models">proportional hazards models</a>, there are a variety of rules of thumb (e.g. 5–9,<sup><a href="#cite_note-Vittinghoff_et_al._(2007)-7">[7]</a></sup> 10<sup><a href="#cite_note-8">[8]</a></sup> and 10–15<sup><a href="#cite_note-9">[9]</a></sup> — the guideline of 10 observations per independent variable is known as the "<a href="/wiki/One_in_ten_rule">one in ten rule</a>"). In the process of regression model selection, the mean squared error of the random regression function can be split into random noise, approximation bias, and variance in the estimate of the regression function. The <a href="/wiki/Bias%E2%80%93variance_tradeoff">bias–variance tradeoff</a> is often used to overcome overfit models.
</p><p>With a large set of <a href="/wiki/Explanatory_variable">explanatory variables</a> that actually have no relation to the <a href="/wiki/Dependent_variable">dependent variable</a> being predicted, some variables will in general be falsely found to be <a href="/wiki/Statistically_significant">statistically significant</a> and the researcher may thus retain them in the model, thereby overfitting the model. This is known as <a href="/wiki/Freedman%27s_paradox">Freedman's paradox</a>.
</p>
<h2>Machine learning[<a href="/w/index.php?title=Overfitting&amp;action=edit&amp;section=3">edit</a>]</h2>
<div><p><a href="/wiki/File:Overfitting_svg.svg"></a></p><div><p>Figure 4. Overfitting/overtraining in supervised learning (e.g., <a href="/wiki/Neural_network">neural network</a>). Training error is shown in blue, validation error in red, both as a function of the number of training cycles. If the validation error increases (positive slope) while the training error steadily decreases (negative slope) then a situation of overfitting may have occurred. The best predictive and fitted model would be where the validation error has its global minimum.</p></div></div>
<p>Usually a learning <a href="/wiki/Algorithm">algorithm</a> is trained using some set of "training data": exemplary situations for which the desired output is known. The goal is that the algorithm will also perform well on predicting the output when fed "validation data" that was not encountered during its training.
</p><p>Overfitting is the use of models or procedures that violate <a href="/wiki/Occam%27s_razor">Occam's razor</a>, for example by including more adjustable parameters than are ultimately optimal, or by using a more complicated approach than is ultimately optimal. For an example where there are too many adjustable parameters, consider a dataset where training data for y can be adequately predicted by a linear function of two independent variables. Such a function requires only three parameters (the intercept and two slopes). Replacing this simple function with a new, more complex quadratic function, or with a new, more complex linear function on more than two independent variables, carries a risk: Occam's razor implies that any given complex function is <i>a priori</i> less probable than any given simple function. If the new, more complicated function is selected instead of the simple function, and if there was not a large enough gain in training-data fit to offset the complexity increase, then the new complex function "overfits" the data, and the complex overfitted function will likely perform worse than the simpler function on validation data outside the training dataset, even though the complex function performed as well, or perhaps even better, on the training dataset.<sup><a href="#cite_note-hawkins-10">[10]</a></sup>
</p><p>When comparing different types of models, complexity cannot be measured solely by counting how many parameters exist in each model; the expressivity of each parameter must be considered as well. For example, it is nontrivial to directly compare the complexity of a neural net (which can track curvilinear relationships) with m parameters to a regression model with n parameters.<sup><a href="#cite_note-hawkins-10">[10]</a></sup>
</p><p>Overfitting is especially likely in cases where learning was performed too long or where training examples are rare, causing the learner to adjust to very specific random features of the training data that have no <a href="/wiki/Causal_relation">causal relation</a> to the <a href="/wiki/Function_approximation">target function</a>. In this process of overfitting, the performance on the training examples still increases while the performance on unseen data becomes worse.
</p><p>As a simple example, consider a database of retail purchases that includes the item bought, the purchaser, and the date and time of purchase. It's easy to construct a model that will fit the training set perfectly by using the date and time of purchase to predict the other attributes, but this model will not generalize at all to new data, because those past times will never occur again.
</p><p>Generally, a learning algorithm is said to overfit relative to a simpler one if it is more accurate in fitting known data (hindsight) but less accurate in predicting new data (foresight). One can intuitively understand overfitting from the fact that information from all past experience can be divided into two groups: information that is relevant for the future, and irrelevant information ("noise"). Everything else being equal, the more difficult a criterion is to predict (i.e., the higher its uncertainty), the more noise exists in past information that needs to be ignored. The problem is determining which part to ignore. A learning algorithm that can reduce the risk of fitting noise is called "<a href="/wiki/Robustness_(computer_science)#Robust_machine_learning">robust</a>."
</p>
<h3>Consequences[<a href="/w/index.php?title=Overfitting&amp;action=edit&amp;section=4">edit</a>]</h3>
<p>The most obvious consequence of overfitting is poor performance on the validation dataset. Other negative consequences include:<sup><a href="#cite_note-hawkins-10">[10]</a></sup>
</p>
<ul><li>A function that is overfitted is likely to request more information about each item in the validation dataset than does the optimal function; gathering this additional unneeded data can be expensive or error-prone, especially if each individual piece of information must be gathered by human observation and manual data-entry.</li>
<li>A more complex, overfitted function is likely to be less portable than a simple one. At one extreme, a one-variable linear regression is so portable that, if necessary, it could even be done by hand. At the other extreme are models that can be reproduced only by exactly duplicating the original modeler's entire setup, making reuse or scientific reproduction difficult.</li></ul>
<h3>Remedy[<a href="/w/index.php?title=Overfitting&amp;action=edit&amp;section=5">edit</a>]</h3>
<p>The optimal function usually needs verification on bigger or completely new datasets. There are, however, methods like <a href="/wiki/Minimum_spanning_tree">minimum spanning tree</a> or <a href="/wiki/Life-time_of_correlation">life-time of correlation</a> that applies the dependence between correlation coefficients and time-series (window width). Whenever the window width is big enough, the correlation coefficients are stable and don't depend on the window width size anymore. Therefore, a correlation matrix can be created by calculating a coefficient of correlation between investigated variables. This matrix can be represented topologically as a complex network where direct and indirect influences between variables are visualized. Dropout regularisation can also improve robustness and therefore reduce over-fitting by probabilistically removing inputs to a layer.
</p>
<h2>Underfitting[<a href="/w/index.php?title=Overfitting&amp;action=edit&amp;section=6">edit</a>]</h2>
<div><p><a href="/wiki/File:Underfitted_Model.png"></a></p><div><p>Figure 5.  The red line represents an underfitted model of the data points represented in blue. We would expect to see a parabola shaped line to represent the curvature of the data points.</p></div></div>
<div><p><a href="/wiki/File:Underfitting_fitted_model.png"></a></p><div><p>Figure 6.  The blue line represents a fitted model of the data points represented in green.</p></div></div>
<p>Underfitting is the inverse of overfitting, meaning that the statistical model or machine learning algorithm is too simplistic to accurately represent the data. A sign of underfitting is that there is a high bias and low variance detected in the current model or algorithm used (the inverse of overfitting: low <a href="/wiki/Bias">bias</a> and high <a href="/wiki/Variance">variance</a>). This can be gathered from the <a href="/wiki/Bias-variance_tradeoff">Bias-variance tradeoff</a> which is the method of analyzing a model or algorithm for bias error, variance error and irreducible error. With a high bias and low variance the result of the model is that it will inaccurately represent the data points and thus insufficiently be able to predict future data results (see <a href="/wiki/Generalization_error">Generalization error</a>). Shown in Figure 5 the linear line could not represent all the given data points due to the line not resembling the curvature of the points. We would expect to see a parabola shaped line as shown in Figure 6 and Figure 1. As previously mentioned if we were to use Figure 5 for analysis we would get false predictive results contrary to the results if we analyzed Figure 6.
</p><p>Burnham &amp; Anderson state the following.<sup><a href="#cite_note-BA2002-3">[3]</a></sup><sup>: 32 </sup>
</p>
<blockquote><p>… an underfitted model would ignore some important replicable (i.e., conceptually replicable in most other samples) structure in the data and thus fail to identify effects that were actually supported by the data. In this case, bias in the parameter estimators is often substantial, and the sampling variance is underestimated, both factors resulting in poor confidence interval coverage. Underfitted models tend to miss important treatment effects in experimental settings.</p></blockquote>
<h3>Resolving underfitting[<a href="/w/index.php?title=Overfitting&amp;action=edit&amp;section=7">edit</a>]</h3>
<p>Resolving underfitting can be handled in multiple ways, a possible method could be to increase the model's parameters, or to add more training data. Adding more training data could be obtained from getting new features from the current features (known as <a href="/wiki/Feature_engineering">Feature engineering</a>). Another possible method would be to move away from the current statistical model or machine learning algorithm to a different one that could better represent the data.
</p>
<h2>See also[<a href="/w/index.php?title=Overfitting&amp;action=edit&amp;section=8">edit</a>]</h2>
<div>
<ul><li><a href="/wiki/Bias%E2%80%93variance_tradeoff">Bias–variance tradeoff</a></li>
<li><a href="/wiki/Curve_fitting">Curve fitting</a></li>
<li><a href="/wiki/Data_dredging">Data dredging</a></li>
<li><a href="/wiki/Feature_selection">Feature selection</a></li>
<li><a href="/wiki/Feature_engineering">Feature engineering</a></li>
<li><a href="/wiki/Freedman%27s_paradox">Freedman's paradox</a></li>
<li><a href="/wiki/Generalization_error">Generalization error</a></li>
<li><a href="/wiki/Goodness_of_fit">Goodness of fit</a></li>
<li><a href="/wiki/Life-time_of_correlation">Life-time of correlation</a></li>
<li><a href="/wiki/Model_selection">Model selection</a></li>
<li><a href="/wiki/Researcher_degrees_of_freedom">Researcher degrees of freedom</a></li>
<li><a href="/wiki/Occam%27s_razor">Occam's razor</a></li>
<li><a href="/wiki/Helmut_Norpoth#&quot;Primary_Model&quot;_for_US_presidential_elections">Primary model</a></li>
<li><a href="/wiki/Vapnik%E2%80%93Chervonenkis_dimension">Vapnik–Chervonenkis dimension</a> – larger VC dimension implies larger risk of overfitting</li></ul>
</div>
<h2>Notes[<a href="/w/index.php?title=Overfitting&amp;action=edit&amp;section=9">edit</a>]</h2>
<div><ol>
<li><b><a href="#cite_ref-1">^</a></b> Definition of "<a href="https://web.archive.org/web/20171107014257/https://en.oxforddictionaries.com/definition/overfitting">overfitting</a>" at <a href="/wiki/OxfordDictionaries.com">OxfordDictionaries.com</a>: this definition is specifically for statistics.
</li>
<li>^ <a href="#cite_ref-CDS_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-CDS_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-CDS_2-2"><sup><i><b>c</b></i></sup></a> Everitt B.S., Skrondal A. (2010), <i>Cambridge Dictionary of Statistics</i>, <a href="/wiki/Cambridge_University_Press">Cambridge University Press</a>.
</li>
<li>^ <a href="#cite_ref-BA2002_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-BA2002_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-BA2002_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-BA2002_3-3"><sup><i><b>d</b></i></sup></a> <cite>Burnham, K. P.; Anderson, D. R. (2002), <i>Model Selection and Multimodel Inference</i> (2nd ed.), Springer-Verlag</cite>.
</li>
<li><b><a href="#cite_ref-4">^</a></b> <cite><a href="/wiki/Gerda_Claeskens">Claeskens, G.</a>; <a href="/wiki/Nils_Lid_Hjort">Hjort, N.L.</a> (2008), <i>Model Selection and Model Averaging</i>, <a href="/wiki/Cambridge_University_Press">Cambridge University Press</a></cite>.
</li>
<li><b><a href="#cite_ref-RMS_5-0">^</a></b> <cite>Harrell, F. E. Jr. (2001), <i>Regression Modeling Strategies</i>, Springer</cite>.
</li>
<li><b><a href="#cite_ref-6">^</a></b> <cite>Martha K. Smith (2014-06-13). <a href="http://www.ma.utexas.edu/users/mks/statmistakes/ovefitting.html">"Overfitting"</a>. <a href="/wiki/University_of_Texas_at_Austin">University of Texas at Austin</a>. Retrieved 2016-07-31.</cite>
</li>
<li><b><a href="#cite_ref-Vittinghoff_et_al._(2007)_7-0">^</a></b> <cite>Vittinghoff, E.; McCulloch, C. E. (2007). <a href="https://doi.org/10.1093%2Faje%2Fkwk052">"Relaxing the Rule of Ten Events per Variable in Logistic and Cox Regression"</a>. <i><a href="/wiki/American_Journal_of_Epidemiology">American Journal of Epidemiology</a></i>. <b>165</b> (6): 710–718. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1093%2Faje%2Fkwk052">10.1093/aje/kwk052</a>. <a href="/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/17182981">17182981</a>.</cite>
</li>
<li><b><a href="#cite_ref-8">^</a></b> <cite>Draper, Norman R.; Smith, Harry (1998). <i>Applied Regression Analysis</i> (3rd ed.). <a href="/wiki/John_Wiley_%26_Sons">Wiley</a>. <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0471170822"><bdi>978-0471170822</bdi></a>.</cite>
</li>
<li><b><a href="#cite_ref-9">^</a></b> <cite>Jim Frost (2015-09-03). <a href="http://blog.minitab.com/blog/adventures-in-statistics/the-danger-of-overfitting-regression-models">"The Danger of Overfitting Regression Models"</a>. Retrieved 2016-07-31.</cite>
</li>
<li>^ <a href="#cite_ref-hawkins_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-hawkins_10-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-hawkins_10-2"><sup><i><b>c</b></i></sup></a> <cite>Hawkins, Douglas M (2004). "The problem of overfitting". <i><a href="/wiki/Journal_of_Chemical_Information_and_Modeling">Journal of Chemical Information and Modeling</a></i>. <b>44</b> (1): 1–12. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1021%2Fci0342472">10.1021/ci0342472</a>. <a href="/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/14741005">14741005</a>.</cite>
</li>
</ol></div>
<h2>References[<a href="/w/index.php?title=Overfitting&amp;action=edit&amp;section=10">edit</a>]</h2>
<ul><li><cite><a href="/wiki/David_Leinweber">Leinweber, D. J.</a> (2007). "Stupid data miner tricks". <i><a href="/wiki/The_Journal_of_Investing">The Journal of Investing</a></i>. <b>16</b>: 15–22. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.3905%2Fjoi.2007.681820">10.3905/joi.2007.681820</a>. <a href="/wiki/S2CID_(identifier)">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:108627390">108627390</a>.</cite></li>
<li><cite>Tetko, I. V.; Livingstone, D. J.; Luik, A. I. (1995). <a href="http://www.vcclab.org/articles/jcics-overtraining.pdf">"Neural network studies. 1. Comparison of Overfitting and Overtraining"</a> (PDF). <i><a href="/wiki/Journal_of_Chemical_Information_and_Modeling">Journal of Chemical Information and Modeling</a></i>. <b>35</b> (5): 826–833. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1021%2Fci00027a006">10.1021/ci00027a006</a>.</cite></li>
<li><i>Tip 7: Minimize overfitting</i>. <cite>Chicco, D. (December 2017). <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5721660">"Ten quick tips for machine learning in computational biology"</a>. <i><a href="/wiki/BioData_Mining">BioData Mining</a></i>. <b>10</b> (35): 35. <a href="/wiki/Doi_(identifier)">doi</a>:<a href="https://doi.org/10.1186%2Fs13040-017-0155-3">10.1186/s13040-017-0155-3</a>. <a href="/wiki/PMC_(identifier)">PMC</a> <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5721660">5721660</a>. <a href="/wiki/PMID_(identifier)">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/29234465">29234465</a>.</cite></li></ul>
<h2>Further reading[<a href="/w/index.php?title=Overfitting&amp;action=edit&amp;section=11">edit</a>]</h2>
<ul><li><cite><a href="/wiki/Brian_Christian">Christian, Brian</a>; Griffiths, Tom (April 2017), "Chapter 7: Overfitting", <i>Algorithms To Live By: The computer science of human decisions</i>, <a href="/wiki/William_Collins_(imprint)">William Collins</a>, pp. 149–168, <a href="/wiki/ISBN_(identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-00-754799-9"><bdi>978-0-00-754799-9</bdi></a></cite></li></ul>
<h2>External links[<a href="/w/index.php?title=Overfitting&amp;action=edit&amp;section=12">edit</a>]</h2>
<ul><li><a href="http://blog.lokad.com/journal/2009/4/22/overfitting-when-accuracy-measure-goes-wrong.html">Overfitting: when accuracy measure goes wrong</a> – introductory video tutorial</li>
<li><a href="http://www3.cs.stonybrook.edu/~skiena/jaialai/excerpts/node16.html">The Problem of Overfitting Data</a> – <a href="/wiki/Stony_Brook_University">Stony Brook University</a></li>
<li><a href="https://statmodeling.stat.columbia.edu/2017/07/15/what-is-overfitting-exactly/">What is "overfitting," exactly?</a> – <a href="/wiki/Andrew_Gelman">Andrew Gelman</a> blog</li>
<li><a href="http://courses.cs.washington.edu/courses/cse546/12wi/slides/cse546wi12LinearRegression.pdf">CSE546: Linear Regression Bias / Variance Tradeoff</a> – <a href="/wiki/University_of_Washington">University of Washington</a></li>
<li><a href="https://towardsdatascience.com/underfitting-and-overfitting-in-machine-learning-and-how-to-deal-with-it-6fe4a8a49dbf">Underfitting and Overfitting in machine learning and how to deal with it !!!</a> – Towards Data Science</li>
<li><a href="https://www.ibm.com/cloud/learn/underfitting">What is Underfitting</a> – <a href="/wiki/IBM">IBM</a></li>
<li><a href="https://www.geeksforgeeks.org/underfitting-and-overfitting-in-machine-learning/">ML | Underfitting and Overfitting</a> – Geeks for Geeks article - Dewang Nautiyal</li></ul>
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 Contents

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 * (Top)
 * 1 Statistical inference
 + 1.1 Regression
 * 2 Machine learning
 + 2.1 Consequences
 + 2.2 Remedy
 * 3 Underfitting
 + 3.1 Resolving underfitting
 * 4 See also
 * 5 Notes
 * 6 References
 * 7 Further reading
 * 8 External links
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 Overfitting

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 From Wikipedia, the free encyclopedia
 This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed.
 Find sources: "Overfitting" – news · newspapers · books · scholar · JSTOR ( August 2017 ) (Learn how and when to remove this template message) 
 
 Part of a series on 
 Machine learning 
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 Figure 1. The green line represents an overfitted model and the black line represents a regularized model. While the green line best follows the training data, it is too dependent on that data and it is likely to have a higher error rate on new unseen data, compared to the black line.
 Figure 2. Noisy (roughly linear) data is fitted to a linear function and a polynomial function. Although the polynomial function is a perfect fit, the linear function can be expected to generalize better: if the two functions were used to extrapolate beyond the fitted data, the linear function should make better predictions.
 Figure 3. The blue dashed line represents an underfitted model. A straight line can never fit a parabola. This model is too simple.

 In mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably".[1] An overfitted model is a mathematical model that contains more parameters than can be justified by the data.[2] The essence of overfitting is to have unknowingly extracted some of the residual variation (i.e., the noise) as if that variation represented underlying model structure.[3] : 45

 Underfitting occurs when a mathematical model cannot adequately capture the underlying structure of the data. An under-fitted model is a model where some parameters or terms that would appear in a correctly specified model are missing.[2] Under-fitting would occur, for example, when fitting a linear model to non-linear data. Such a model will tend to have poor predictive performance.

 The possibility of over-fitting exists because the criterion used for selecting the model is not the same as the criterion used to judge the suitability of a model. For example, a model might be selected by maximizing its performance on some set of training data, and yet its suitability might be determined by its ability to perform well on unseen data; then over-fitting occurs when a model begins to "memorize" training data rather than "learning" to generalize from a trend.

 As an extreme example, if the number of parameters is the same as or greater than the number of observations, then a model can perfectly predict the training data simply by memorizing the data in its entirety. (For an illustration, see Figure 2.) Such a model, though, will typically fail severely when making predictions.

 The potential for overfitting depends not only on the number of parameters and data but also the conformability of the model structure with the data shape, and the magnitude of model error compared to the expected level of noise or error in the data.[ citation needed ] Even when the fitted model does not have an excessive number of parameters, it is to be expected that the fitted relationship will appear to perform less well on a new data set than on the data set used for fitting (a phenomenon sometimes known as shrinkage).[2] In particular, the value of the coefficient of determination will shrink relative to the original data.

 To lessen the chance or amount of overfitting, several techniques are available (e.g., model comparison, cross-validation, regularization, early stopping, pruning, Bayesian priors, or dropout). The basis of some techniques is either (1) to explicitly penalize overly complex models or (2) to test the model's ability to generalize by evaluating its performance on a set of data not used for training, which is assumed to approximate the typical unseen data that a model will encounter.

 Statistical inference [ edit ]

 This section needs expansion. You can help by adding to it. ( October 2017 )
 

 In statistics, an inference is drawn from a statistical model, which has been selected via some procedure. Burnham & Anderson, in their much-cited text on model selection, argue that to avoid overfitting, we should adhere to the "Principle of Parsimony".[3] The authors also state the following.[3] : 32–33

 Overfitted models … are often free of bias in the parameter estimators, but have estimated (and actual) sampling variances that are needlessly large (the precision of the estimators is poor, relative to what could have been accomplished with a more parsimonious model). False treatment effects tend to be identified, and false variables are included with overfitted models. … A best approximating model is achieved by properly balancing the errors of underfitting and overfitting.

 Overfitting is more likely to be a serious concern when there is little theory available to guide the analysis, in part because then there tend to be a large number of models to select from. The book Model Selection and Model Averaging (2008) puts it this way.[4]

 Given a data set, you can fit thousands of models at the push of a button, but how do you choose the best? With so many candidate models, overfitting is a real danger. Is the monkey who typed Hamlet actually a good writer?

 Regression [ edit ]

 In regression analysis, overfitting occurs frequently.[5] As an extreme example, if there are p variables in a linear regression with p data points, the fitted line can go exactly through every point.[6] For logistic regression or Cox proportional hazards models, there are a variety of rules of thumb (e.g. 5–9,[7] 10[8] and 10–15[9] — the guideline of 10 observations per independent variable is known as the "one in ten rule"). In the process of regression model selection, the mean squared error of the random regression function can be split into random noise, approximation bias, and variance in the estimate of the regression function. The bias–variance tradeoff is often used to overcome overfit models.

 With a large set of explanatory variables that actually have no relation to the dependent variable being predicted, some variables will in general be falsely found to be statistically significant and the researcher may thus retain them in the model, thereby overfitting the model. This is known as Freedman's paradox.

 Machine learning [ edit ]

 Figure 4. Overfitting/overtraining in supervised learning (e.g., neural network). Training error is shown in blue, validation error in red, both as a function of the number of training cycles. If the validation error increases (positive slope) while the training error steadily decreases (negative slope) then a situation of overfitting may have occurred. The best predictive and fitted model would be where the validation error has its global minimum.

 Usually a learning algorithm is trained using some set of "training data": exemplary situations for which the desired output is known. The goal is that the algorithm will also perform well on predicting the output when fed "validation data" that was not encountered during its training.

 Overfitting is the use of models or procedures that violate Occam's razor, for example by including more adjustable parameters than are ultimately optimal, or by using a more complicated approach than is ultimately optimal. For an example where there are too many adjustable parameters, consider a dataset where training data for y can be adequately predicted by a linear function of two independent variables. Such a function requires only three parameters (the intercept and two slopes). Replacing this simple function with a new, more complex quadratic function, or with a new, more complex linear function on more than two independent variables, carries a risk: Occam's razor implies that any given complex function is a priori less probable than any given simple function. If the new, more complicated function is selected instead of the simple function, and if there was not a large enough gain in training-data fit to offset the complexity increase, then the new complex function "overfits" the data, and the complex overfitted function will likely perform worse than the simpler function on validation data outside the training dataset, even though the complex function performed as well, or perhaps even better, on the training dataset.[10]

 When comparing different types of models, complexity cannot be measured solely by counting how many parameters exist in each model; the expressivity of each parameter must be considered as well. For example, it is nontrivial to directly compare the complexity of a neural net (which can track curvilinear relationships) with m parameters to a regression model with n parameters.[10]

 Overfitting is especially likely in cases where learning was performed too long or where training examples are rare, causing the learner to adjust to very specific random features of the training data that have no causal relation to the target function. In this process of overfitting, the performance on the training examples still increases while the performance on unseen data becomes worse.

 As a simple example, consider a database of retail purchases that includes the item bought, the purchaser, and the date and time of purchase. It's easy to construct a model that will fit the training set perfectly by using the date and time of purchase to predict the other attributes, but this model will not generalize at all to new data, because those past times will never occur again.

 Generally, a learning algorithm is said to overfit relative to a simpler one if it is more accurate in fitting known data (hindsight) but less accurate in predicting new data (foresight). One can intuitively understand overfitting from the fact that information from all past experience can be divided into two groups: information that is relevant for the future, and irrelevant information ("noise"). Everything else being equal, the more difficult a criterion is to predict (i.e., the higher its uncertainty), the more noise exists in past information that needs to be ignored. The problem is determining which part to ignore. A learning algorithm that can reduce the risk of fitting noise is called "robust."

 Consequences [ edit ]

 The most obvious consequence of overfitting is poor performance on the validation dataset. Other negative consequences include:[10]

 * A function that is overfitted is likely to request more information about each item in the validation dataset than does the optimal function; gathering this additional unneeded data can be expensive or error-prone, especially if each individual piece of information must be gathered by human observation and manual data-entry.
 * A more complex, overfitted function is likely to be less portable than a simple one. At one extreme, a one-variable linear regression is so portable that, if necessary, it could even be done by hand. At the other extreme are models that can be reproduced only by exactly duplicating the original modeler's entire setup, making reuse or scientific reproduction difficult.

 Remedy [ edit ]

 The optimal function usually needs verification on bigger or completely new datasets. There are, however, methods like minimum spanning tree or life-time of correlation that applies the dependence between correlation coefficients and time-series (window width). Whenever the window width is big enough, the correlation coefficients are stable and don't depend on the window width size anymore. Therefore, a correlation matrix can be created by calculating a coefficient of correlation between investigated variables. This matrix can be represented topologically as a complex network where direct and indirect influences between variables are visualized. Dropout regularisation can also improve robustness and therefore reduce over-fitting by probabilistically removing inputs to a layer.

 Underfitting [ edit ]

 Figure 5. The red line represents an underfitted model of the data points represented in blue. We would expect to see a parabola shaped line to represent the curvature of the data points.
 Figure 6. The blue line represents a fitted model of the data points represented in green.

 Underfitting is the inverse of overfitting, meaning that the statistical model or machine learning algorithm is too simplistic to accurately represent the data. A sign of underfitting is that there is a high bias and low variance detected in the current model or algorithm used (the inverse of overfitting: low bias and high variance). This can be gathered from the Bias-variance tradeoff which is the method of analyzing a model or algorithm for bias error, variance error and irreducible error. With a high bias and low variance the result of the model is that it will inaccurately represent the data points and thus insufficiently be able to predict future data results (see Generalization error). Shown in Figure 5 the linear line could not represent all the given data points due to the line not resembling the curvature of the points. We would expect to see a parabola shaped line as shown in Figure 6 and Figure 1. As previously mentioned if we were to use Figure 5 for analysis we would get false predictive results contrary to the results if we analyzed Figure 6.

 Burnham & Anderson state the following.[3] : 32

 … an underfitted model would ignore some important replicable (i.e., conceptually replicable in most other samples) structure in the data and thus fail to identify effects that were actually supported by the data. In this case, bias in the parameter estimators is often substantial, and the sampling variance is underestimated, both factors resulting in poor confidence interval coverage. Underfitted models tend to miss important treatment effects in experimental settings.

 Resolving underfitting [ edit ]

 This section does not cite any sources. Please help improve this section by adding citations to reliable sources . Unsourced material may be challenged and removed . ( January 2022 ) (Learn how and when to remove this template message)
 

 Resolving underfitting can be handled in multiple ways, a possible method could be to increase the model's parameters, or to add more training data. Adding more training data could be obtained from getting new features from the current features (known as Feature engineering). Another possible method would be to move away from the current statistical model or machine learning algorithm to a different one that could better represent the data.

 See also [ edit ]

 * Bias–variance tradeoff
 * Curve fitting
 * Data dredging
 * Feature selection
 * Feature engineering
 * Freedman's paradox
 * Generalization error
 * Goodness of fit
 * Life-time of correlation
 * Model selection
 * Researcher degrees of freedom
 * Occam's razor
 * Primary model
 * Vapnik–Chervonenkis dimension – larger VC dimension implies larger risk of overfitting

 Notes [ edit ]

 1. ^ Definition of " overfitting " at OxfordDictionaries.com : this definition is specifically for statistics.
 2. ^ a b c Everitt B.S., Skrondal A. (2010), Cambridge Dictionary of Statistics , Cambridge University Press .
 3. ^ a b c d Burnham, K. P.; Anderson, D. R. (2002), Model Selection and Multimodel Inference (2nd ed.), Springer-Verlag .
 4. ^ Claeskens, G.; Hjort, N.L. (2008), Model Selection and Model Averaging, Cambridge University Press .
 5. ^ Harrell, F. E. Jr. (2001), Regression Modeling Strategies, Springer .
 6. ^ Martha K. Smith (2014-06-13). "Overfitting". University of Texas at Austin . Retrieved 2016-07-31 .
 7. ^ Vittinghoff, E.; McCulloch, C. E. (2007). "Relaxing the Rule of Ten Events per Variable in Logistic and Cox Regression". American Journal of Epidemiology. 165 (6): 710–718. doi:10.1093/aje/kwk052. PMID 17182981.
 8. ^ Draper, Norman R.; Smith, Harry (1998). Applied Regression Analysis (3rd ed.). Wiley. ISBN 978-0471170822.
 9. ^ Jim Frost (2015-09-03). "The Danger of Overfitting Regression Models" . Retrieved 2016-07-31 .
 10. ^ a b c Hawkins, Douglas M (2004). "The problem of overfitting". Journal of Chemical Information and Modeling. 44 (1): 1–12. doi:10.1021/ci0342472. PMID 14741005.

 References [ edit ]

 * Leinweber, D. J. (2007). "Stupid data miner tricks". The Journal of Investing. 16: 15–22. doi:10.3905/joi.2007.681820. S2CID 108627390.
 * Tetko, I. V.; Livingstone, D. J.; Luik, A. I. (1995). "Neural network studies. 1. Comparison of Overfitting and Overtraining" (PDF) . Journal of Chemical Information and Modeling. 35 (5): 826–833. doi:10.1021/ci00027a006.
 * Tip 7: Minimize overfitting. Chicco, D. (December 2017). "Ten quick tips for machine learning in computational biology". BioData Mining. 10 (35): 35. doi:10.1186/s13040-017-0155-3. PMC 5721660. PMID 29234465.

 Further reading [ edit ]

 * Christian, Brian; Griffiths, Tom (April 2017), "Chapter 7: Overfitting", Algorithms To Live By: The computer science of human decisions, William Collins, pp. 149–168, ISBN 978-0-00-754799-9

 External links [ edit ]

 * Overfitting: when accuracy measure goes wrong – introductory video tutorial
 * The Problem of Overfitting Data – Stony Brook University
 * What is "overfitting," exactly? – Andrew Gelman blog
 * CSE546: Linear Regression Bias / Variance Tradeoff – University of Washington
 * Underfitting and Overfitting in machine learning and how to deal with it !!! – Towards Data Science
 * What is Underfitting – IBM
 * ML | Underfitting and Overfitting – Geeks for Geeks article - Dewang Nautiyal
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From Wikipedia, the free encyclopedia
	 
      Figure 1.  The green line represents an overfitted model and the black line represents a regularized model. While the green line best follows the training data, it is too dependent on that data and it is likely to have a higher error rate on new unseen data, compared to the black line.  
      Figure 2.  Noisy (roughly linear) data is fitted to a linear function and a polynomial function. Although the polynomial function is a perfect fit, the linear function can be expected to generalize better: if the two functions were used to extrapolate beyond the fitted data, the linear function should make better predictions.  
      Figure 3.  The blue dashed line represents an underfitted model. A straight line can never fit a parabola. This model is too simple.  
In mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably". [1]  An overfitted model is a mathematical model that contains more parameters than can be justified by the data. [2]  The essence of overfitting is to have unknowingly extracted some of the residual variation (i.e., the noise) as if that variation represented underlying model structure. [3]  : 45 
  Underfitting occurs when a mathematical model cannot adequately capture the underlying structure of the data. An under-fitted model is a model where some parameters or terms that would appear in a correctly specified model are missing. [2]  Under-fitting would occur, for example, when fitting a linear model to non-linear data. Such a model will tend to have poor predictive performance.
 The possibility of over-fitting exists because the criterion used for selecting the model is not the same as the criterion used to judge the suitability of a model. For example, a model might be selected by maximizing its performance on some set of training data, and yet its suitability might be determined by its ability to perform well on unseen data; then over-fitting occurs when a model begins to "memorize" training data rather than "learning" to generalize from a trend. 
 As an extreme example, if the number of parameters is the same as or greater than the number of observations, then a model can perfectly predict the training data simply by memorizing the data in its entirety. (For an illustration, see Figure 2.) Such a model, though, will typically fail severely when making predictions. 
 The potential for overfitting depends not only on the number of parameters and data but also the conformability of the model structure with the data shape, and the magnitude of model error compared to the expected level of noise or error in the data.[ citation needed ] Even when the fitted model does not have an excessive number of parameters, it is to be expected that the fitted relationship will appear to perform less well on a new data set than on the data set used for fitting (a phenomenon sometimes known as shrinkage). [2]  In particular, the value of the coefficient of determination will shrink relative to the original data.
 To lessen the chance or amount of overfitting, several techniques are available (e.g., model comparison, cross-validation, regularization, early stopping, pruning, Bayesian priors, or dropout). The basis of some techniques is either (1) to explicitly penalize overly complex models or (2) to test the model's ability to generalize by evaluating its performance on a set of data not used for training, which is assumed to approximate the typical unseen data that a model will encounter.
Statistical inference[edit]
        This section needs expansion. You can help by adding to it. (October 2017)     
In statistics, an inference is drawn from a statistical model, which has been selected via some procedure. Burnham &amp; Anderson, in their much-cited text on model selection, argue that to avoid overfitting, we should adhere to the "Principle of Parsimony". [3]  The authors also state the following. [3]  : 32–33 
 Overfitted models … are often free of bias in the parameter estimators, but have estimated (and actual) sampling variances that are needlessly large (the precision of the estimators is poor, relative to what could have been accomplished with a more parsimonious model). False treatment effects tend to be identified, and false variables are included with overfitted models. … A best approximating model is achieved by properly balancing the errors of underfitting and overfitting. 
Overfitting is more likely to be a serious concern when there is little theory available to guide the analysis, in part because then there tend to be a large number of models to select from. The book Model Selection and Model Averaging (2008) puts it this way. [4] 
 Given a data set, you can fit thousands of models at the push of a button, but how do you choose the best? With so many candidate models, overfitting is a real danger. Is the monkey who typed Hamlet actually a good writer? 
Regression[edit]
In regression analysis, overfitting occurs frequently. [5]  As an extreme example, if there are p variables in a linear regression with p data points, the fitted line can go exactly through every point. [6]  For logistic regression or Cox proportional hazards models, there are a variety of rules of thumb (e.g. 5–9, [7]  10 [8]  and 10–15 [9]  — the guideline of 10 observations per independent variable is known as the "one in ten rule"). In the process of regression model selection, the mean squared error of the random regression function can be split into random noise, approximation bias, and variance in the estimate of the regression function. The bias–variance tradeoff is often used to overcome overfit models.
 With a large set of explanatory variables that actually have no relation to the dependent variable being predicted, some variables will in general be falsely found to be statistically significant and the researcher may thus retain them in the model, thereby overfitting the model. This is known as Freedman's paradox.
Machine learning[edit]
      Figure 4. Overfitting/overtraining in supervised learning (e.g., neural network). Training error is shown in blue, validation error in red, both as a function of the number of training cycles. If the validation error increases (positive slope) while the training error steadily decreases (negative slope) then a situation of overfitting may have occurred. The best predictive and fitted model would be where the validation error has its global minimum.  
Usually a learning algorithm is trained using some set of "training data": exemplary situations for which the desired output is known. The goal is that the algorithm will also perform well on predicting the output when fed "validation data" that was not encountered during its training.
 Overfitting is the use of models or procedures that violate Occam's razor, for example by including more adjustable parameters than are ultimately optimal, or by using a more complicated approach than is ultimately optimal. For an example where there are too many adjustable parameters, consider a dataset where training data for y can be adequately predicted by a linear function of two independent variables. Such a function requires only three parameters (the intercept and two slopes). Replacing this simple function with a new, more complex quadratic function, or with a new, more complex linear function on more than two independent variables, carries a risk: Occam's razor implies that any given complex function is a priori less probable than any given simple function. If the new, more complicated function is selected instead of the simple function, and if there was not a large enough gain in training-data fit to offset the complexity increase, then the new complex function "overfits" the data, and the complex overfitted function will likely perform worse than the simpler function on validation data outside the training dataset, even though the complex function performed as well, or perhaps even better, on the training dataset. [10] 
 When comparing different types of models, complexity cannot be measured solely by counting how many parameters exist in each model; the expressivity of each parameter must be considered as well. For example, it is nontrivial to directly compare the complexity of a neural net (which can track curvilinear relationships) with m parameters to a regression model with n parameters. [10] 
 Overfitting is especially likely in cases where learning was performed too long or where training examples are rare, causing the learner to adjust to very specific random features of the training data that have no causal relation to the target function. In this process of overfitting, the performance on the training examples still increases while the performance on unseen data becomes worse.
 As a simple example, consider a database of retail purchases that includes the item bought, the purchaser, and the date and time of purchase. It's easy to construct a model that will fit the training set perfectly by using the date and time of purchase to predict the other attributes, but this model will not generalize at all to new data, because those past times will never occur again.
 Generally, a learning algorithm is said to overfit relative to a simpler one if it is more accurate in fitting known data (hindsight) but less accurate in predicting new data (foresight). One can intuitively understand overfitting from the fact that information from all past experience can be divided into two groups: information that is relevant for the future, and irrelevant information ("noise"). Everything else being equal, the more difficult a criterion is to predict (i.e., the higher its uncertainty), the more noise exists in past information that needs to be ignored. The problem is determining which part to ignore. A learning algorithm that can reduce the risk of fitting noise is called "robust."
Consequences[edit]
The most obvious consequence of overfitting is poor performance on the validation dataset. Other negative consequences include: [10] 
 A function that is overfitted is likely to request more information about each item in the validation dataset than does the optimal function; gathering this additional unneeded data can be expensive or error-prone, especially if each individual piece of information must be gathered by human observation and manual data-entry.
A more complex, overfitted function is likely to be less portable than a simple one. At one extreme, a one-variable linear regression is so portable that, if necessary, it could even be done by hand. At the other extreme are models that can be reproduced only by exactly duplicating the original modeler's entire setup, making reuse or scientific reproduction difficult. 
Remedy[edit]
The optimal function usually needs verification on bigger or completely new datasets. There are, however, methods like minimum spanning tree or life-time of correlation that applies the dependence between correlation coefficients and time-series (window width). Whenever the window width is big enough, the correlation coefficients are stable and don't depend on the window width size anymore. Therefore, a correlation matrix can be created by calculating a coefficient of correlation between investigated variables. This matrix can be represented topologically as a complex network where direct and indirect influences between variables are visualized. Dropout regularisation can also improve robustness and therefore reduce over-fitting by probabilistically removing inputs to a layer.
Underfitting[edit]
      Figure 5.  The red line represents an underfitted model of the data points represented in blue. We would expect to see a parabola shaped line to represent the curvature of the data points.  
      Figure 6.  The blue line represents a fitted model of the data points represented in green.  
Underfitting is the inverse of overfitting, meaning that the statistical model or machine learning algorithm is too simplistic to accurately represent the data. A sign of underfitting is that there is a high bias and low variance detected in the current model or algorithm used (the inverse of overfitting: low bias and high variance). This can be gathered from the Bias-variance tradeoff which is the method of analyzing a model or algorithm for bias error, variance error and irreducible error. With a high bias and low variance the result of the model is that it will inaccurately represent the data points and thus insufficiently be able to predict future data results (see Generalization error). Shown in Figure 5 the linear line could not represent all the given data points due to the line not resembling the curvature of the points. We would expect to see a parabola shaped line as shown in Figure 6 and Figure 1. As previously mentioned if we were to use Figure 5 for analysis we would get false predictive results contrary to the results if we analyzed Figure 6.
 Burnham &amp; Anderson state the following. [3]  : 32 
 … an underfitted model would ignore some important replicable (i.e., conceptually replicable in most other samples) structure in the data and thus fail to identify effects that were actually supported by the data. In this case, bias in the parameter estimators is often substantial, and the sampling variance is underestimated, both factors resulting in poor confidence interval coverage. Underfitted models tend to miss important treatment effects in experimental settings. 
Resolving underfitting[edit]
Resolving underfitting can be handled in multiple ways, a possible method could be to increase the model's parameters, or to add more training data. Adding more training data could be obtained from getting new features from the current features (known as Feature engineering). Another possible method would be to move away from the current statistical model or machine learning algorithm to a different one that could better represent the data.
See also[edit]
  Bias–variance tradeoff 
 Curve fitting 
 Data dredging 
 Feature selection 
 Feature engineering 
 Freedman's paradox 
 Generalization error 
 Goodness of fit 
 Life-time of correlation 
 Model selection 
 Researcher degrees of freedom 
 Occam's razor 
 Primary model 
 Vapnik–Chervonenkis dimension – larger VC dimension implies larger risk of overfitting 
Notes[edit]
 
  ^  Definition of "overfitting" at OxfordDictionaries.com: this definition is specifically for statistics.
^    a       b       c    Everitt B.S., Skrondal A. (2010), Cambridge Dictionary of Statistics, Cambridge University Press.
^    a       b       c       d    Burnham, K. P.; Anderson, D. R. (2002), Model Selection and Multimodel Inference (2nd ed.), Springer-Verlag.
  ^   Claeskens, G.; Hjort, N.L. (2008), Model Selection and Model Averaging, Cambridge University Press .
  ^  Harrell, F. E. Jr. (2001), Regression Modeling Strategies, Springer.
  ^  Martha K. Smith (2014-06-13). "Overfitting". University of Texas at Austin. Retrieved 2016-07-31.
  ^  Vittinghoff, E.; McCulloch, C. E. (2007). "Relaxing the Rule of Ten Events per Variable in Logistic and Cox Regression".  American Journal of Epidemiology . 165 (6): 710–718. doi:10.1093/aje/kwk052. PMID 17182981.
  ^  Draper, Norman R.; Smith, Harry (1998). Applied Regression Analysis (3rd ed.). Wiley. ISBN  978-0471170822 .
  ^  Jim Frost (2015-09-03). "The Danger of Overfitting Regression Models". Retrieved 2016-07-31.
^    a       b       c    Hawkins, Douglas M (2004). "The problem of overfitting".  Journal of Chemical Information and Modeling . 44 (1): 1–12. doi:10.1021/ci0342472. PMID 14741005.
 
References[edit]
   Leinweber, D. J. (2007). "Stupid data miner tricks".  The Journal of Investing . 16: 15–22. doi:10.3905/joi.2007.681820. S2CID 108627390. 
 Tetko, I. V.; Livingstone, D. J.; Luik, A. I. (1995). "Neural network studies. 1. Comparison of Overfitting and Overtraining" (PDF).  Journal of Chemical Information and Modeling . 35 (5): 826–833. doi:10.1021/ci00027a006. 
 Tip 7: Minimize overfitting. Chicco, D. (December 2017). "Ten quick tips for machine learning in computational biology".  BioData Mining . 10 (35): 35. doi:10.1186/s13040-017-0155-3. PMC 5721660. PMID 29234465.  
Further reading[edit]
   Christian, Brian; Griffiths, Tom (April 2017), "Chapter 7: Overfitting", Algorithms To Live By: The computer science of human decisions, William Collins, pp. 149–168, ISBN  978-0-00-754799-9    
External links[edit]
  Overfitting: when accuracy measure goes wrong – introductory video tutorial
 The Problem of Overfitting Data – Stony Brook University 
 What is "overfitting," exactly? – Andrew Gelman blog
 CSE546: Linear Regression Bias / Variance Tradeoff – University of Washington 
 Underfitting and Overfitting in machine learning and how to deal with it !!! – Towards Data Science
 What is Underfitting – IBM 
 ML | Underfitting and Overfitting – Geeks for Geeks article - Dewang Nautiyal
Overfitting - Wikipedia
https://en.wikipedia.org/wiki/Overfitting
https://www.reddit.com/r/MachineLearning/comments/3b3dmn/a_cleaned_wikipedia_dataset/
r/MachineLearning - A cleaned wikipedia dataset
2023-02-06
None
<div><div><p>I am doing some research on sequence generators, and I am in need of a cleaned wikipedia dataset- meaning that all the links, images, side notes should be removed and only the textual content should be present. Can anybody provide a link to such an dataset?</p><p>Failing that, can you tell me how to develop such a dataset from scratch? Thanks.</p></div>||||I|||| Press J to jump to the feed. Press question mark to learn the rest of the keyboard shortcuts
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 Posted by 8 years ago

 A cleaned wikipedia dataset

 I am doing some research on sequence generators, and I am in need of a cleaned wikipedia dataset- meaning that all the links, images, side notes should be removed and only the textual content should be present. Can anybody provide a link to such an dataset?

 Failing that, can you tell me how to develop such a dataset from scratch? Thanks.

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 level 1
 · 8 yr. ago

 Have a look at http://blog.lateral.io/2015/06/the-unknown-perils-of-mining-wikipedia/

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 level 2
 · 8 yr. ago

 This is a fantastic link. Thanks for sharing this!

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 level 1
 · 8 yr. ago · edited 8 yr. ago

 This will provide you with a .bz2 file of the English version of wikipedia, so there are no images. Then this Wikipedia Extractor should clean it up in the way you are looking for.

 edit:grammar

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 [deleted]
 · 8 yr. ago

 Thanks for the extractor link-- Really helpful to know this exists....

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 level 1
 · 8 yr. ago

 You might be able to leverage genism's code for this: https://github.com/piskvorky/gensim/blob/develop/gensim/corpora/wikicorpus.py

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 level 1
 · 8 yr. ago

 There's also WikiClean, which I've found to do a good job of removing unnecessary markup. (Whether that's useful for you depends on the task you want to perform.)

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 Op · 8 yr. ago

 I do want that. Can you post a sample of the data it gives as an output. Or maybe PM me. Thanks.

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 level 1
 · 8 yr. ago

 The Polyglot project has clean, preprocessed versions of Wikipedia in a bunch of languages. Extremely useful if you don't want to spend time cleaning stuff up! The English version has about 1.7 billion tokens, so it's not really small either.

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 level 1
 · 8 yr. ago

 If I were going create a dataset like that from scratch, I would use a HTML parsing tool like BeautifulSoup in Python. BeautifulSoup is great for web scraping but you'll still need to do some work cleaning it up.

 I'm not sure how you would go about getting the URLs for all the articles. Maybe many many calls to the [random] (https://en.wikipedia.org/wiki/Special:Random) page while tracking which you have visited.

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 level 2
 · 8 yr. ago

 Wikipedia explicitly says that they would prefer if people didn't scrape their site. They provide torrents of all their articles AND talk sections AND images. The packages combined are around 10GB, unzipping to about 14TB. See https://en.wikipedia.org/wiki/Wikipedia:Database_download

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 level 1
 · 8 yr. ago

 You could also look into something like Beautiful Soup. Parsing out those tags that you don't want shouldn't be too tough.

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 level 1
 · 8 yr. ago

 Also, why bother with wikipedia only. Check out some of the datasets here, like Google ngrams and the Common Crawl. You'll find more data than you need there...

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 Op · 8 yr. ago

 I need to use wikipedia because the word vectors that I use(Glove) are based on that

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I am doing some research on sequence generators, and I am in need of a cleaned wikipedia dataset- meaning that all the links, images, side notes should be removed and only the textual content should be present. Can anybody provide a link to such an dataset? Failing that, can you tell me how to develop such a dataset from scratch? Thanks.
r/MachineLearning - A cleaned wikipedia dataset
https://www.reddit.com/r/MachineLearning/comments/3b3dmn/a_cleaned_wikipedia_dataset/
https://blog.paperspace.com/artificial-intelligence-wiki/
The Artificial Intelligence Wiki | Paperspace Blog
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 We made the AI Wiki to keep the world of artificial intelligence a little less daunting. With easy-to-understand definitions and helpful graphics, the AI Wiki explains dozens of topics in AI, machine learning and deep learning, for beginners and practitioners alike.
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 We made the AI Wiki to keep the world of artificial intelligence a little less daunting. With easy-to-understand definitions and helpful graphics, the AI Wiki explains dozens of topics in AI, machine learning and deep learning, for beginners and practitioners alike.

 3 years ago • 1 min read

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 The world of AI can be overwhelming. Defining one word often involves three others you also didn't know, and by the time you feel comfortable with one concept you've added 10 more to your list of things-to-look-into.

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Introducing The AI Wiki 🧠
 
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 The world of AI can be overwhelming. Defining one word often involves three others you also didn't know, and by the time you feel comfortable with one concept you've added 10 more to your list of things-to-look-into. We made the AI Wiki for exactly those reasons. This is a resource for anybody entering the field, as well as experienced practitioners who need a quick refresher on a certain topic. Do you know what a TPU is? Are you ever confused between the correct number of epochs, iterations, and batch size? How about the difference between machine learning, deep learning, and data science? Equipped with easy-to-understand definitions and helpful graphics, the AI Wiki answers questions like these and dozens more. Think we missed something? Submit a comment or idea here, or reach out on our Community board.
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<h2>From today's featured article</h2>
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<p><a href="/wiki/File:Gold_dinar_of_al-Hafiz_li-Din_Allah,_AH_544.png"></a></p></div>
<p><b><a href="/wiki/Al-Hafiz">Al-Hafiz</a></b> (<abbr>c.</abbr> 1075 – 1149) was the eleventh <a href="/wiki/Caliphate">caliph</a> of the <a href="/wiki/Fatimid_Caliphate">Fatimids</a> from 1132 until his death. He rose to power as <a href="/wiki/Regent">regent</a> after his cousin <a href="/wiki/Al-Amir_bi-Ahkam_Allah">al-Amir</a> was killed in 1130 leaving an infant son. The army seized power, imprisoning al-Hafiz, but he was freed a year later. In 1132, he proclaimed himself caliph and <a href="/wiki/Imamate_in_Ismaili_doctrine">imam</a>. Many <a href="/wiki/Isma%27ilism">Isma'ili</a> followers abroad refused to <a href="/wiki/Hafizi_Isma%27ilism">recognize him as imam</a>, breaking away as the <a href="/wiki/Tayyibi_Isma%27ilism">Tayyibi</a> sect. There were repeated uprisings even in Egypt, although his reign saw little foreign aggression. He tried to restrain his overmighty <a href="/wiki/Vizier_(Fatimid_Caliphate)">viziers</a>, with mixed success. He was repeatedly forced to give way to the demands of various military factions, and although for the last decade of his reign he ruled without a vizier, he was ultimately unable to halt the evolution of the vizierate into a <i>de facto</i> <a href="/wiki/Sultan">sultanate</a>, independent of the caliph. His successors would be reduced to puppets at the hands of powerful viziers, until the end of the Fatimid Caliphate in 1171. (<b><a href="/wiki/Al-Hafiz">Full article...</a></b>)
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<p><a href="/wiki/File:Al%C3%A8xia_Putellas_mural_163033.jpg"></a></p></div>
<ul><li>... that street artist <b><a href="/wiki/TVBoy">TVBoy</a></b>, known for his murals of footballers in Barcelona <i>(example pictured)</i>, painted uplifting art in regions of <a href="/wiki/Kyiv_Oblast">Kyiv</a> ahead of the one-year anniversary of the <a href="/wiki/Russian_invasion_of_Ukraine">2022 Russian invasion</a>?</li>
<li>... that <b><a href="/wiki/Foster_Loyer">Foster Loyer</a></b> broke <a href="/wiki/Michigan_High_School_Athletic_Association">Michigan's high-school</a> and <a href="/wiki/Stephen_Curry">Steph Curry</a>'s <a href="/wiki/Davidson_Wildcats_men%27s_basketball">Davidson</a> records for consecutive <a href="/wiki/Free_throw">free throws</a>?</li>
<li>... that the <b><a href="/wiki/2023_United_Kingdom_pupil_protests">2023 United Kingdom pupil protests</a></b> were organised on TikTok and Snapchat?</li>
<li>... that at the age of 27 New Zealand entrepreneur <b><a href="/wiki/Jamie_Beaton">Jamie Beaton</a></b> had degrees from Harvard, Stanford, Oxford, and <a href="/wiki/Tsinghua_University">Tsinghua University</a>, and was working on his seventh degree, from Yale?</li>
<li>... that <i><b><a href="/wiki/It_Was_Hot,_We_Stayed_in_the_Water">It Was Hot, We Stayed in the Water</a></b></i> explores the theme of water and was inspired by <a href="/wiki/Phil_Elverum">Phil Elverum</a>'s visits to the ocean?</li>
<li>... that in 1956 <a href="/wiki/Green_Bay_Packers">Green Bay Packers</a> athletic trainer <b><a href="/wiki/Bud_Jorgensen">Bud Jorgensen</a></b> became the first athletic trainer selected by the <a href="/wiki/National_Football_League">National Football League</a> to treat players at a <a href="/wiki/Pro_Bowl">Pro Bowl</a>?</li>
<li>... that the <b><a href="/wiki/St._Raphael_Provincial_Park">St. Raphael Provincial Park</a></b> in <a href="/wiki/Northern_Ontario">Northern Ontario</a>, Canada, is part of the 1,530 km<sup>2</sup> (590 sq mi) St. Raphael Signature Site, which is recognized for its natural and recreational values?</li>
<li>... that in the 1970s, residents of <b><a href="/wiki/The_Belnord">the Belnord</a></b> in New York City had to sneak in refrigerators at night?</li></ul>
</div>
</div>
<div>
<h2>In the news</h2>
<div><div>
<p><a href="/wiki/File:Jon_Rahm_(cropped).png"></a></p><p>Jon Rahm</p></div>
<ul><li>In the <a href="/wiki/Myanmar_civil_war_(2021%E2%80%93present)">Myanmar civil war</a>, the <a href="/wiki/State_Administration_Council">military junta</a>'s air force <b><a href="/wiki/Pazigyi_massacre">kills</a></b> at least 130 civilians in <a href="/wiki/Pazigyi">Pazigyi</a>.</li>
<li>In <a href="/wiki/Golf">golf</a>, <a href="/wiki/Jon_Rahm">Jon Rahm</a> <i>(pictured)</i> wins <b><a href="/wiki/2023_Masters_Tournament">the Masters Tournament</a></b>.</li>
<li>Former U.S. president <a href="/wiki/Donald_Trump">Donald Trump</a> <b><a href="/wiki/Indictment_of_Donald_Trump">is arraigned</a></b> on 34 charges of falsifying business records.</li>
<li>Finland <b><a href="/wiki/Finland%E2%80%93NATO_relations">joins</a></b> <a href="/wiki/NATO">NATO</a> as its <a href="/wiki/Enlargement_of_NATO">31st member</a>.</li>
<li>In <b><a href="/wiki/2023_Andorran_parliamentary_election">the Andorran parliamentary election</a></b>, the liberal coalition, led by Prime Minister <a href="/wiki/Xavier_Espot_Zamora">Xavier Espot</a>, wins an absolute majority of seats in the <a href="/wiki/General_Council_(Andorra)">General Council</a>.</li></ul>
</div>
<h2>On this day</h2>
<div>
<p><b><a href="/wiki/April_13">April 13</a></b>: <b><a href="/wiki/Qadr_Night">Night of Decree</a></b> (<a href="/wiki/Shia_Islam">Shia Islam</a>, 2023)
</p>
<div>
<p><a href="/wiki/File:Jefferson_Memorial_At_Dusk_1.jpg"></a></p><p>Jefferson Memorial</p></div>
<ul><li><a href="/wiki/1742">1742</a> – German-British composer <a href="/wiki/George_Frideric_Handel">George Frideric Handel</a>'s celebrated <a href="/wiki/Oratorio">oratorio</a> <i><b><a href="/wiki/Messiah_(Handel)">Messiah</a></b></i> was first performed in <a href="/wiki/Dublin">Dublin</a>.</li>
<li><a href="/wiki/1943">1943</a> – The <a href="/wiki/Neoclassical_architecture">Neoclassical</a> <b><a href="/wiki/Jefferson_Memorial">Jefferson Memorial</a></b> <i>(pictured)</i> in Washington, D.C., was formally dedicated on the 200th anniversary of <a href="/wiki/Thomas_Jefferson">Thomas Jefferson</a>'s birth.</li>
<li><a href="/wiki/1946">1946</a> – <b><a href="/wiki/Nakam">Nakam</a></b>, a Jewish organization seeking revenge for <a href="/wiki/The_Holocaust">the Holocaust</a>, attempted to poison thousands of <a href="/wiki/Schutzstaffel">SS</a> prisoners at <a href="/wiki/Stalag_XIII-D">Langwasser internment camp</a>, but did not kill anyone.</li>
<li><a href="/wiki/1953">1953</a> – <a href="/wiki/Ian_Fleming">Ian Fleming</a>'s novel <i><b><a href="/wiki/Casino_Royale_(novel)">Casino Royale</a></b></i> was published as the first work to feature his British spy character <b><a href="/wiki/James_Bond_(literary_character)">James Bond</a></b>.</li>
<li><a href="/wiki/2017">2017</a> – <a href="/wiki/War_in_Afghanistan_(2001%E2%80%932021)">War in Afghanistan</a>: In <b><a href="/wiki/2017_Nangarhar_airstrike">an airstrike</a></b> in <a href="/wiki/Nangarhar_Province">Nangarhar Province</a>, the U.S. military dropped <b><a href="/wiki/GBU-43/B_MOAB">the most powerful conventional bomb ever used in combat</a></b>.</li></ul>
<div><ul><li><b><a href="/wiki/Arthur_Matthew_Weld_Downing">Arthur Matthew Weld Downing</a></b> (<abbr>b.</abbr> 1850)</li><li><b><a href="/wiki/Joe_Hewitt_(RAAF_officer)">Joe Hewitt</a></b> (<abbr>b.</abbr> 1901)</li><li><b><a href="/wiki/Evelyne_Daitz">Evelyne Daitz</a></b> (<abbr>b.</abbr> 1936)</li></ul></div>
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<h2>Today's featured picture</h2>
<div>
<table>
<tbody><tr>
<td><a href="/wiki/File:Spiti_River_Kaza_Himachal_Jun18_D72_7232.jpg"></a>
</td></tr>
<tr>
<td>
<p><b><a href="/wiki/Spiti">Spiti</a></b> is a high-altitude <a href="/wiki/Desert_climate#Cold_desert_climates">cold desert</a> in the <a href="/wiki/Western_Himalayas">Western Himalayas</a> in India. "Spiti" means "the middle land", between <a href="/wiki/Tibet">Tibet</a> and India. The region is above the <a href="/wiki/Tree_line">tree line</a>, with only shrubs and a few scattered stunted trees. In the upper valley, the braided Spiti River flows in narrow channels in a very wide river bed, as seen in this photograph, taken just above <a href="/wiki/Kaza,_Himachal_Pradesh">Kaza</a>, the largest town in Spiti. In the lower valley, the river meanders through gorges 10 to 130 metres (33 to 427 ft) deep that it has cut in the <a href="/wiki/Sedimentary_rock">sedimentary</a> deposits. The Moravian geologist <a href="/wiki/Ferdinand_Stoliczka">Ferdinand Stoliczka</a> discovered a major geological formation near the village of <a href="/wiki/Mud_village,_Spiti#Geology">Mud</a> in the 1860s, and identified a number of layers or successions. The people of Spiti follow <a href="/wiki/Tibetan_Buddhism">Tibetan Buddhism</a>, and their culture is similar to those of neighbouring Tibet and Ladakh. The region is known for adventure tourism, trekking and mountaineering.
</p>
<p><small>Photograph credit: <a href="/wiki/Timothy_A._Gonsalves">Timothy A. Gonsalves</a></small></p>
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 Welcome to Wikipedia

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 Gold dinar of al-Hafiz

 Al-Hafiz (c. 1075 – 1149) was the eleventh caliph of the Fatimids from 1132 until his death. He rose to power as regent after his cousin al-Amir was killed in 1130 leaving an infant son. The army seized power, imprisoning al-Hafiz, but he was freed a year later. In 1132, he proclaimed himself caliph and imam. Many Isma'ili followers abroad refused to recognize him as imam, breaking away as the Tayyibi sect. There were repeated uprisings even in Egypt, although his reign saw little foreign aggression. He tried to restrain his overmighty viziers, with mixed success. He was repeatedly forced to give way to the demands of various military factions, and although for the last decade of his reign he ruled without a vizier, he was ultimately unable to halt the evolution of the vizierate into a de facto sultanate, independent of the caliph. His successors would be reduced to puppets at the hands of powerful viziers, until the end of the Fatimid Caliphate in 1171. (Full article...)

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 TVBoy mural of Alexia Putellas
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 * ... that Foster Loyer broke Michigan's high-school and Steph Curry's Davidson records for consecutive free throws?
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 * ... that It Was Hot, We Stayed in the Water explores the theme of water and was inspired by Phil Elverum's visits to the ocean?
 * ... that in 1956 Green Bay Packers athletic trainer Bud Jorgensen became the first athletic trainer selected by the National Football League to treat players at a Pro Bowl?
 * ... that the St. Raphael Provincial Park in Northern Ontario, Canada, is part of the 1,530 km2 (590 sq mi) St. Raphael Signature Site, which is recognized for its natural and recreational values?
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 Jon Rahm
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 April 13: Night of Decree (Shia Islam, 2023)

 Jefferson Memorial
 * 1742 – German-British composer George Frideric Handel's celebrated oratorio Messiah was first performed in Dublin.
 * 1943 – The Neoclassical Jefferson Memorial (pictured) in Washington, D.C., was formally dedicated on the 200th anniversary of Thomas Jefferson's birth.
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 * 2017 – War in Afghanistan: In an airstrike in Nangarhar Province, the U.S. military dropped the most powerful conventional bomb ever used in combat.
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 Today's featured picture

               
 Spiti is a high-altitude cold desert in the Western Himalayas in India. "Spiti" means "the middle land", between Tibet and India. The region is above the tree line, with only shrubs and a few scattered stunted trees. In the upper valley, the braided Spiti River flows in narrow channels in a very wide river bed, as seen in this photograph, taken just above Kaza, the largest town in Spiti. In the lower valley, the river meanders through gorges 10 to 130 metres (33 to 427 ft) deep that it has cut in the sedimentary deposits. The Moravian geologist Ferdinand Stoliczka discovered a major geological formation near the village of Mud in the 1860s, and identified a number of layers or successions. The people of Spiti follow Tibetan Buddhism, and their culture is similar to those of neighbouring Tibet and Ladakh. The region is known for adventure tourism, trekking and mountaineering.
               
 Photograph credit: Timothy A. Gonsalves              
               
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From Wikipedia, the free encyclopedia
	
	
From today's featured article
 
    
  Al-Hafiz  (c. 1075 – 1149) was the eleventh caliph of the Fatimids from 1132 until his death. He rose to power as regent after his cousin al-Amir was killed in 1130 leaving an infant son. The army seized power, imprisoning al-Hafiz, but he was freed a year later. In 1132, he proclaimed himself caliph and imam. Many Isma'ili followers abroad refused to recognize him as imam, breaking away as the Tayyibi sect. There were repeated uprisings even in Egypt, although his reign saw little foreign aggression. He tried to restrain his overmighty viziers, with mixed success. He was repeatedly forced to give way to the demands of various military factions, and although for the last decade of his reign he ruled without a vizier, he was ultimately unable to halt the evolution of the vizierate into a de facto sultanate, independent of the caliph. His successors would be reduced to puppets at the hands of powerful viziers, until the end of the Fatimid Caliphate in 1171. ( Full article... )
Did you know ...
    
 ... that street artist  TVBoy , known for his murals of footballers in Barcelona (example pictured), painted uplifting art in regions of Kyiv ahead of the one-year anniversary of the 2022 Russian invasion?
... that  Foster Loyer  broke Michigan's high-school and Steph Curry's Davidson records for consecutive free throws?
... that the  2023 United Kingdom pupil protests  were organised on TikTok and Snapchat?
... that at the age of 27 New Zealand entrepreneur  Jamie Beaton  had degrees from Harvard, Stanford, Oxford, and Tsinghua University, and was working on his seventh degree, from Yale?
... that   It Was Hot, We Stayed in the Water   explores the theme of water and was inspired by Phil Elverum's visits to the ocean?
... that in 1956 Green Bay Packers athletic trainer  Bud Jorgensen  became the first athletic trainer selected by the National Football League to treat players at a Pro Bowl?
... that the  St. Raphael Provincial Park  in Northern Ontario, Canada, is part of the 1,530 km2 (590 sq mi) St. Raphael Signature Site, which is recognized for its natural and recreational values?
... that in the 1970s, residents of  the Belnord  in New York City had to sneak in refrigerators at night? 
In the news
 
    Jon Rahm 
 In the Myanmar civil war, the military junta's air force  kills  at least 130 civilians in Pazigyi.
In golf, Jon Rahm (pictured) wins  the Masters Tournament .
Former U.S. president Donald Trump  is arraigned  on 34 charges of falsifying business records.
Finland  joins  NATO as its 31st member.
In  the Andorran parliamentary election , the liberal coalition, led by Prime Minister Xavier Espot, wins an absolute majority of seats in the General Council. 
On this day
  April 13 :  Night of Decree  (Shia Islam, 2023)
    Jefferson Memorial 
  1742 – German-British composer George Frideric Handel's celebrated oratorio   Messiah   was first performed in Dublin.
 1943 – The Neoclassical  Jefferson Memorial  (pictured) in Washington, D.C., was formally dedicated on the 200th anniversary of Thomas Jefferson's birth.
 1946 –  Nakam , a Jewish organization seeking revenge for the Holocaust, attempted to poison thousands of SS prisoners at Langwasser internment camp, but did not kill anyone.
 1953 – Ian Fleming's novel   Casino Royale   was published as the first work to feature his British spy character  James Bond .
 2017 – War in Afghanistan: In  an airstrike  in Nangarhar Province, the U.S. military dropped  the most powerful conventional bomb ever used in combat . 
    Arthur Matthew Weld Downing  (b. 1850)   Joe Hewitt  (b. 1901)   Evelyne Daitz  (b. 1936)  
Today's featured picture
 
  
 
  Spiti  is a high-altitude cold desert in the Western Himalayas in India. "Spiti" means "the middle land", between Tibet and India. The region is above the tree line, with only shrubs and a few scattered stunted trees. In the upper valley, the braided Spiti River flows in narrow channels in a very wide river bed, as seen in this photograph, taken just above Kaza, the largest town in Spiti. In the lower valley, the river meanders through gorges 10 to 130 metres (33 to 427 ft) deep that it has cut in the sedimentary deposits. The Moravian geologist Ferdinand Stoliczka discovered a major geological formation near the village of Mud in the 1860s, and identified a number of layers or successions. The people of Spiti follow Tibetan Buddhism, and their culture is similar to those of neighbouring Tibet and Ladakh. The region is known for adventure tourism, trekking and mountaineering.
 Photograph credit: Timothy A. Gonsalves  
    
Other areas of Wikipedia
   Community portal  – The central hub for editors, with resources, links, tasks, and announcements.
  Village pump  – Forum for discussions about Wikipedia itself, including policies and technical issues.
  Site news  – Sources of news about Wikipedia and the broader Wikimedia movement.
  Teahouse  – Ask basic questions about using or editing Wikipedia.
  Help desk  – Ask questions about using or editing Wikipedia.
  Reference desk  – Ask research questions about encyclopedic topics.
  Content portals  – A unique way to navigate the encyclopedia. 
Wikipedia's sister projects
Wikipedia is written by volunteer editors and hosted by the Wikimedia Foundation, a non-profit organization that also hosts a range of other volunteer projects:
    
 
    
 
    
  Meta-Wiki Wikimedia project coordination
    
 
    
 
    
 
    
 
    
 
    
 
    
 
    
 
    
 
 
Wikipedia languages
This Wikipedia is written in English. Many other Wikipedias are available; some of the largest are listed below.
 
  العربية 
 Deutsch 
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 Français 
 Italiano 
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 Svenska 
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  Asturianu 
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 ไทย
Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Main_Page
https://www.mediawiki.org/wiki/MediaWiki
MediaWiki
2004-08-06
None
<div><div>
<p></p><h2>MediaWiki is a collaboration and documentation platform brought to you by a vibrant community.</h2><p></p>
<p>The MediaWiki software is used by <a href="/wiki/Special:MyLanguage/Sites_using_MediaWiki">tens of thousands of websites</a> and <a href="/wiki/Special:MyLanguage/MediaWiki_testimonials">thousands of companies and organizations</a>.
It powers Wikipedia and also this website.
MediaWiki helps you collect and organize knowledge and make it available to people.
It's powerful, <a href="/wiki/Special:MyLanguage/Localisation">multilingual</a>, <a href="https://en.wikipedia.org/wiki/FLOSS">free and open</a>, extensible, customizable, reliable, and free of charge.
<a href="/wiki/Special:MyLanguage/Manual:What_is_MediaWiki%3F">Find out more</a> and <a href="/wiki/Special:MyLanguage/Manual:Deciding_whether_to_use_a_wiki_as_your_website_type">if MediaWiki is right for you</a>.
</p>
<div>
	<div>
	<h3>Set up and run MediaWiki</h3>
	</div>
	<div>
	<h3>Edit and use MediaWiki</h3>
	</div>
	<div>
	<h3>Develop and extend code</h3>
	</div>
</div>
<div>
	<div>
	<h3>Get help and contribute</h3>
	<div>
<ul><li>Cannot find the answer to a problem with MediaWiki? Ask the <a href="/wiki/Project:Support_desk">support desk</a>!</li>
<li><a href="/wiki/Special:MyLanguage/How_to_contribute">Get involved</a> as a translator, designer, documentation writer, tester, tech ambassador, or developer</li>
<li><a href="/wiki/Special:MyLanguage/How_to_report_a_bug">Report wrong software behavior or a feature proposal</a></li></ul>
	</div>
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	<div>
	<h3>News</h3>
	
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 From mediawiki.org

 MediaWiki is a collaboration and documentation platform brought to you by a vibrant community.

 Photo of participants of the Wikimedia Hackathon 2019

 The MediaWiki software is used by tens of thousands of websites and thousands of companies and organizations. It powers Wikipedia and also this website. MediaWiki helps you collect and organize knowledge and make it available to people. It's powerful, multilingual, free and open, extensible, customizable, reliable, and free of charge. Find out more and if MediaWiki is right for you.

 Set up and run MediaWiki

 * Download, install and configure MediaWiki
 * Add functionality by installing extensions
 * Problems? See errors and symptoms and FAQ
 * Don't own a server? Find hosting services
 * Get professional development and consulting
 * Join MediaWiki Stakeholders user group

 Edit and use MediaWiki

 * Learn how to navigate
 * Learn how to edit a page
 * Learn more about reading, editing, and personal customization

 Develop and extend code

 * Read the MediaWiki developer documentation
 * Visit the Wikimedia Developer Portal

 Get help and contribute

 * Cannot find the answer to a problem with MediaWiki? Ask the support desk!
 * Get involved as a translator, designer, documentation writer, tester, tech ambassador, or developer
 * Report wrong software behavior or a feature proposal

 News

 2023-03-30 MediaWiki 1.35.10, 1.38.6 and 1.39.3 security releases are now available. 2023-04-19 to 2023-04-21 EMWCon in Austin, Texas, United States. 2023-05-19 to 2023-05-21 Wikimedia Hackathon in Athens, Greece (Europe). 2023-03-11 MediaWiki is now on Mastodon! Follow us for updates at @mediawiki@wikis.world

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 English • Afrikaans • العربية • asturianu • беларуская • беларуская (тарашкевіца) • български • বাংলা • bosanski • català • کوردی • čeština • dansk • Deutsch • español • فارسی • suomi • français • ગુજરાતી • עברית • हिन्दी • hrvatski • magyar • հայերեն • Bahasa Indonesia • italiano • 日本語 • Jawa • қазақша • 한국어 • Bahasa Melayu • Mirandés • Nederlands • polski • português • português do Brasil • română • русский • sardu • සිංහල • slovenčina • slovenščina • Soomaaliga • shqip • српски / srpski • svenska • ไทย • Türkçe • українська • Tiếng Việt • 粵語 • 中文


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 * 
MediaWiki is a collaboration and documentation platform brought to you by a vibrant community.  
The MediaWiki software is used by tens of thousands of websites and thousands of companies and organizations.
It powers Wikipedia and also this website.
MediaWiki helps you collect and organize knowledge and make it available to people.
It's powerful, multilingual, free and open, extensible, customizable, reliable, and free of charge.
Find out more and if MediaWiki is right for you.
	
	Set up and run MediaWiki
	
	
	Edit and use MediaWiki
	
	
	Develop and extend code
	
	
	Get help and contribute
	
 Cannot find the answer to a problem with MediaWiki? Ask the support desk!
 Get involved as a translator, designer, documentation writer, tester, tech ambassador, or developer
 Report wrong software behavior or a feature proposal  
	
	
	
	News
MediaWiki
https://www.mediawiki.org/wiki/MediaWiki
https://www.mediawiki.org/wiki/New_Developers
New Developers - MediaWiki
2017-07-06
None
<div><div><div><p>Languages:</p><ul><li><a href="/wiki/New_Developers/af">Afrikaans</a></li>
<li><a href="/wiki/New_Developers/id">Bahasa Indonesia</a></li>
<li><a href="/wiki/New_Developers/nan">Bân-lâm-gú</a></li>
<li><a href="/wiki/New_Developers/de">Deutsch</a></li>
<li>English</li>
<li><a href="/wiki/New_Developers/ca">català</a></li>
<li><a href="/wiki/New_Developers/es">español</a></li>
<li><a href="/wiki/New_Developers/fr">français</a></li>
<li><a href="/wiki/New_Developers/pl">polski</a></li>
<li><a href="/wiki/New_Developers/pt">português</a></li>
<li><a href="/wiki/New_Developers/pt-br">português do Brasil</a></li>
<li><a href="/wiki/New_Developers/fi">suomi</a></li>
<li><a href="/wiki/New_Developers/cs">čeština</a></li>
<li><a href="/wiki/New_Developers/be-tarask">беларуская (тарашкевіца)</a></li>
<li><a href="/wiki/New_Developers/ru">русский</a></li>
<li><a href="/wiki/New_Developers/he">עברית</a></li>
<li><a href="/wiki/New_Developers/ar">العربية</a></li>
<li><a href="/wiki/New_Developers/fa">فارسی</a></li>
<li><a href="/wiki/New_Developers/hi">हिन्दी</a></li>
<li><a href="/wiki/New_Developers/bn">বাংলা</a></li>
<li><a href="/wiki/New_Developers/zh">中文</a></li>
<li><a href="/wiki/New_Developers/ja">日本語</a></li>
<li><a href="/wiki/New_Developers/ko">한국어</a></li></ul></div>
<p>This page explains how to get started as a developer who wants to contribute to <a href="/wiki/Special:MyLanguage/Differences_between_Wikipedia,_Wikimedia,_MediaWiki,_and_wiki">Wikimedia</a> technical projects.
</p>
<p></p><h2>Welcome!</h2><p></p>
<figure><a href="/wiki/File:Wikimedia_Hackathon_Prague_2019_-_Group_Photo_-_CLK.png"></a><figcaption>Participants of the <a href="/wiki/Special:MyLanguage/Wikimedia_Hackathon_2019">Wikimedia Hackathon 2019</a></figcaption></figure>
<p><a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/Wikimedia_movement">Wikimedia</a>'s technical community always welcomes new contributors!
</p><p>Become part of a global community, and help make access to free knowledge easier for everyone!
</p>
<p></p><h2>How to start contributing</h2><p></p>
<p>The following steps are a general outline of how to get started contributing:
</p>
<ol><li>Learn <a href="#Some_basics_to_know">the basics of how Wikimedia open source software projects work</a>.</li>
<li>Read the <a href="#Communication">Communication guidelines</a>.</li>
<li>Set up accounts: <a href="/wiki/Special:MyLanguage/Developer_account">Create a developer account</a>. Depending on the type of contribution you want to make, you may also need to set up accounts in <a href="/wiki/Special:MyLanguage/Phabricator/Help">Phabricator</a>, and <a href="/wiki/Special:MyLanguage/Gerrit/Tutorial">set up Git and Gerrit</a>.</li>
<li><a href="#Choose_a_software_project">Choose a software project</a>.</li>
<li>Choose and solve a task (write and test your code).</li>
<li>Submit your code changes for review. Follow the <a href="/wiki/Special:MyLanguage/Gerrit/Code_review/Getting_reviews">Guide to getting your code reviewed</a> and <a href="/wiki/Special:MyLanguage/Gerrit/Tutorial#Submit_a_patch">submit a patch</a>.</li></ol>
<p>The rest of this guide provides additional details about the process.
</p>
<p></p><h2>Basics of how Wikimedia software projects work</h2><p></p>
<p>Wikimedia has software projects in <a href="https://commons.wikimedia.org/wiki/File:Slides_from_Wikipedia_session_at_LibrePlanet_2019.pdf">many different areas</a>. 
</p><p>The maintainers of each software project choose the infrastructure they prefer. In general, most software projects have: 
</p>
<ul><li>a <b>task tracking</b> tool where software bugs and enhancement requests are reported, managed and discussed. Examples are <a href="/wiki/Special:MyLanguage/Phabricator">Wikimedia Phabricator</a>, GitHub, or <a href="/wiki/Special:MyLanguage/GitLab">Wikimedia GitLab</a>.</li>
<li>a <b>code repository</b> where the source code can be "checked out" to everybody. Examples are <a href="/wiki/Special:MyLanguage/Gerrit">Wikimedia Gerrit</a>, GitHub, or <a href="/wiki/Special:MyLanguage/GitLab">Wikimedia GitLab</a>.</li>
<li>a <b>code review</b> tool where proposed code changes ("patches") get discussed and improved. Examples are Wikimedia Git/Gerrit, GitHub, or GitLab. After your proposed patch is approved and merged into the code repository, your code changes become available to everybody.</li>
<li>general <b>places for discussion</b> of the software project and for help and support. Those places can be mailing lists, IRC chat channels, wiki pages, or other places. The exact places depend on each project.</li></ul>
<p>At any point, if you run into problems or need help, please ask. To ask good questions in the right places, follow the <a href="#communication">"communication tips"</a>.
</p>
<p></p><h2>Contributing to software in MediaWiki</h2><p></p>
<p>Are you a user of a MediaWiki wiki looking to add a feature fix a bug in one?
Please see <a href="/wiki/Finding_software_in_MediaWiki">Finding software in MediaWiki</a> to learn how to find the location of the software project that you are looking to contribute to.
</p>
<p></p><h2>Overview of technical areas</h2><p></p>
<p>For an overview of Wikimedia technology and examples of the major areas where developers can contribute, visit <a href="/wiki/New_Developers/Introduction_to_the_Wikimedia_Technical_Ecosystem"> Introduction to the Wikimedia Technical Ecosystem</a>.
</p>
<p></p><h2>Choose a software project</h2><p></p>
<p>The following projects offer resources, mentorship, and are looking for new developers to contribute to them.
Choose one of the following projects and follow the project's documentation to set up your development environment, choose a task to work on, solve the task, and submit your code changes for review.
You are free to contribute to these projects or any others you are interested in related to Wikimedia.
Most can be found by searching for them on <a href="/wiki/Special:MyLanguage/Phabricator">Phabricator</a> or online.
</p>
<p><i>Are you a maintainer and want your project to be included in the list of software projects above? <a href="/wiki/New_Developers/Featured_Projects">Find out more and join!</a></i>
</p>
<p></p><h2>Outreach programs and single tasks</h2><p></p>
<p>In addition to the recommended software projects above, there are more ways to choose a project or task to work on:
</p>
<div>
<div>
	<h3><a href="/wiki/File:GSoC-icon-192.png"></a> <a href="/wiki/Special:MyLanguage/Outreach_programs">Outreach programs</a></h3>
	<p>Wikimedia offers internships in programs such as Google Summer of Code and Outreachy.</p></div>
<div>
	<h3><a href="/wiki/File:Bug_icon_-_Noun_project_198.svg"></a> <a href="/wiki/Special:MyLanguage/Good_first_bugs">Good first tasks</a></h3>
	<p>There are many single tasks (across many software projects) that are suitable for newcomers.<br />However, mentors may not be available for these tasks, and your proposed patches may not receive fast reviews.</p></div></div> 
<p></p><h2>Communication tips</h2><p></p>
<p>Follow these tips to communicate effectively and get help from community members.
</p>
<h3>Use Phabricator tasks effectively</h3>
<p>When you plan to work on a <a href="/wiki/Phabricator">Phabricator</a> task:
</p>
<ul><li><b>No need to ask for permission:</b> You can work on unassigned tasks without asking someone to assign them to you. There is no authority who assigns tasks or who needs to be asked first.
<ul><li>If a task already has a recent patch in Gerrit, choose a different task to work on instead.</li>
<li>If an existing patch in Gerrit has not been merged and has not seen any changes for a long time, you could <a href="/wiki/Special:MyLanguage/Gerrit/Tutorial#Amending_a_change_(your_own_or_someone_else's)">improve that existing patch</a>, based on the feedback in Gerrit and in the task.</li></ul></li>
<li><b>Do your research:</b> When you consider working on a task, do research before you start coding. Look at the code, try to understand what it is supposed to do, read related documentation, and try to find the places where you need to make code changes.
<ul><li>In a <a href="/wiki/Special:MyLanguage/Phabricator">Phabricator</a> task, use the project tags in the side bar to find the code repository for the task.</li>
<li>If you have no idea at all how to fix the bug, consider finding an easier one first.</li></ul></li>
<li>You do not need to <b>announce your plans</b> before you start working on a task, but you should communicate that you are working on the task.
<ul><li>When you start work, <b>set yourself as task assignee</b> by clicking <i>Edit Task…</i> in Phabricator, and set your Phabricator username in the <i>Assigned To</i> field. This communicates to others that you are working on it, so they don't duplicate work.</li>
<li><b>When your plans or interests change:</b> If you are no longer working on a task, remove yourself as the assignee of the task. This tells others that they can work on the task, and they won't expect you to still work on it.</li></ul></li>
<li>Follow <a href="/wiki/Special:MyLanguage/Bug_management/Phabricator_etiquette">Phabricator etiquette</a>.
<ul><li>In Phabricator tasks, discuss only specific questions about the topic of that task. Don't use Phabricator to ask general questions, like how to set up a development environment or how to fix problems with Gerrit.</li></ul></li></ul>
<h3>Compose good questions</h3>
<ul><li><a href="https://dontasktoask.com/">Don't ask to ask...just ask!</a>.</li>
<li><b>Be specific and provide context:</b> Instead of simply asking "Can you give me more info?", "Please guide me", or "Please tell me how to start", include the following information in your question:
<ul><li>What are you trying to achieve?</li>
<li>What have you already tried? Copy and paste your commands and their output (if not too long) instead of paraphrasing in your own words.</li>
<li>What have you found out already during your research? Include links to code, documentation, or other resources you already consulted.</li></ul></li>
<li>Use specific titles and subject lines in your communication. "Proposal draft" or "Need help" is not specific.</li>
<li><b>Keep conversations readable:</b> When you reply in <a href="/wiki/Special:MyLanguage/Outreach_programs/Zulip">Zulip</a>, in Phabricator tasks, or on mailing lists, only quote sections of previous comments that are relevant to your response. If you quote a <i>complete</i> previous comment, it makes threads hard to read.</li></ul>
<h3>Follow communication policies and best practices</h3>
<p>Before you send or post your question:
</p>
<ul><li>Read and follow the <a href="/wiki/Special:MyLanguage/Code_of_Conduct">code of conduct for Wikimedia technical spaces</a>.</li>
<li><b>Use <a href="/wiki/Special:MyLanguage/inclusive_language">Inclusive language</a>:</b> Instead of using terms that assume a gender identity (like "<a href="https://heyguys.cc/">guys</a>", "madam", or "sir") use the name of the person instead.</li></ul>
<h3>Ask in the right place</h3>
<ul><li><b>Ask in public:</b> Do not send private messages if your conversation topic is not secret. Private messages don't help others.</li>
<li><b>Ask and discuss in the best place:</b>
<ul><li>In Phabricator tasks, discuss only specific questions about the topic of that task.</li>
<li>Ask general technical questions, like how to set up a development environment or how to fix problems with Gerrit, in the places listed on <a href="/wiki/Special:MyLanguage/Communication">Communication</a>.</li>
<li>If you take part in an <a href="/wiki/Special:MyLanguage/Outreach_programs">outreach program</a>, then <a href="/wiki/Special:MyLanguage/Outreach_programs/Zulip">Zulip</a> is for discussing questions about the outreach programs themselves.</li></ul></li></ul>
<h3>Be patient</h3>
<p>After you post your question:
</p>
<ul><li>Do not ask people for code review in a separate message. People receive Gerrit and Phabricator notifications and will respond when they can.</li>
<li>When seeking input and comments, especially during weekends and holidays, you may need to wait until business hours resume. On chat channels like IRC: if nobody answers, try again at a different time; don't just give up!</li>
<li>If you don't get an answer even after waiting and being patient, consider if other <a href="/wiki/Special:MyLanguage/Communication">Communication channels</a> might be a better place to ask your question.</li></ul>
<p></p><h2>Additional resources</h2><p></p>
<ul><li><a href="/wiki/New_Developers/Introduction_to_the_Wikimedia_Technical_Ecosystem"> Introduction to the Wikimedia Technical Ecosystem</a> provides an overview of Wikimedia tech, focused on the major areas where developers can contribute.</li>
<li><a href="/wiki/Special:MyLanguage/How_to_contribute">How to contribute</a> lists many more ways to contribute, including areas like documentation, testing, and more.</li>
<li><a href="/wiki/Special:MyLanguage/How_to_become_a_MediaWiki_hacker">How to become a MediaWiki hacker</a>: For developers who want to work on MediaWiki core or MediaWiki extensions.</li>
<li><a href="/wiki/Special:MyLanguage/Developer_hub">Developer hub</a>: More resources for established Wikimedia developers.</li>
<li>To ask your questions and to join general discussions, check the places listed on <a href="/wiki/Special:MyLanguage/Communication">Communication</a>.</li>
<li><a href="/wiki/Wikimedia_tutorials">Wikimedia tutorials</a>: An index of tutorials that feature various languages, APIs, and frameworks in the Wikimedia technology stack.</li></ul>
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 * Beginning
 * 1 Welcome!
 * 2 How to start contributing
 * 3 Basics of how Wikimedia software projects work
 * 4 Contributing to software in MediaWiki
 * 5 Overview of technical areas
 * 6 Choose a software project
 + 6.1
 + 6.2 Commons App for Android
 + 6.3 Wiki Education Dashboard
 + 6.4 Pywikibot
 + 6.5
 + 6.6 VideoCutTool
 * 7 Outreach programs and single tasks
 + 7.1 Outreach programs
 + 7.2 Good first tasks
 * 8 Communication tips
 + 8.1 Use Phabricator tasks effectively
 + 8.2 Compose good questions
 + 8.3 Follow communication policies and best practices
 + 8.4 Ask in the right place
 + 8.5 Be patient
 * 9 Additional resources
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 * 한국어

 This page explains how to get started as a developer who wants to contribute to Wikimedia technical projects.

 Welcome!

 Participants of the Wikimedia Hackathon 2019

 Wikimedia's technical community always welcomes new contributors!

 Become part of a global community, and help make access to free knowledge easier for everyone!

 How to start contributing

 The following steps are a general outline of how to get started contributing:

 1. Learn the basics of how Wikimedia open source software projects work.
 2. Read the Communication guidelines.
 3. Set up accounts: Create a developer account. Depending on the type of contribution you want to make, you may also need to set up accounts in Phabricator, and set up Git and Gerrit.
 4. Choose a software project.
 5. Choose and solve a task (write and test your code).
 6. Submit your code changes for review. Follow the Guide to getting your code reviewed and submit a patch.

 The rest of this guide provides additional details about the process.

 Basics of how Wikimedia software projects work

 Wikimedia has software projects in many different areas.

 The maintainers of each software project choose the infrastructure they prefer. In general, most software projects have:

 * a task tracking tool where software bugs and enhancement requests are reported, managed and discussed. Examples are Wikimedia Phabricator, GitHub, or Wikimedia GitLab.
 * a code repository where the source code can be "checked out" to everybody. Examples are Wikimedia Gerrit, GitHub, or Wikimedia GitLab.
 * a code review tool where proposed code changes ("patches") get discussed and improved. Examples are Wikimedia Git/Gerrit, GitHub, or GitLab. After your proposed patch is approved and merged into the code repository, your code changes become available to everybody.
 * general places for discussion of the software project and for help and support. Those places can be mailing lists, IRC chat channels, wiki pages, or other places. The exact places depend on each project.

 At any point, if you run into problems or need help, please ask. To ask good questions in the right places, follow the "communication tips".

 Contributing to software in MediaWiki

 Are you a user of a MediaWiki wiki looking to add a feature fix a bug in one? Please see Finding software in MediaWiki to learn how to find the location of the software project that you are looking to contribute to.

 Overview of technical areas

 For an overview of Wikimedia technology and examples of the major areas where developers can contribute, visit Introduction to the Wikimedia Technical Ecosystem.

 Choose a software project

 The following projects offer resources, mentorship, and are looking for new developers to contribute to them. Choose one of the following projects and follow the project's documentation to set up your development environment, choose a task to work on, solve the task, and submit your code changes for review. You are free to contribute to these projects or any others you are interested in related to Wikimedia. Most can be found by searching for them on Phabricator or online.

 An offline reader for people without internet access

 * Skills required: Java/Kotlin (Android), Swift (iOS), Qt (desktop), NodeJS (mediawiki offliner), C++
 * Get in touch: Mailing list / Slack here
 * Get the source code: GitHub
 * Read the general documentation and the README.md file of the corresponding project
 * Check the recommended tasks to work on: Android, iOS, JS, mwoffliner on GitHub
 * Mentor(s): Matthieu Gauthier, Emmanuel Engelhart, Stephane Coillet-Matillon

 Commons App for Android

 An app for Android devices to upload your pictures to Wikimedia Commons

 * Skills required: Java
 * Get in touch: Google Groups
 * Get the source code: GitHub
 * Read the documentation
 * Check the recommended tasks to work on: GitHub
 * Mentor(s): Josephine Lim

 Wiki Education Dashboard

 A web application that supports Wikipedia education assignments, provides data and course management for instructors and students

 * Skills required: Ruby, JavaScript
 * Get in touch: #wikimedia-ed connect on irc.libera.chat
 * Get the source code: GitHub
 * Read the documentation
 * Check the recommended tasks to work on: GitHub
 * Mentor(s): Sage Ross

 Pywikibot

 A Python library and collection of scripts that automate work on MediaWiki sites.

 * Skills required: Python
 * Get in touch: #pywikibot connect on irc.libera.chat / Mailing list
 * Get the source code: Use git to get the source code
 * Read the documentation and API reference
 * Check the recommended tasks to work on: Phabricator
 * Mentor(s): xqt

 Scribe provides Wikidata based keyboards for second language learners. Features include translation, verb conjugation and noun-gender annotation. This project is very open to those who want to learn the needed languages and how to work with Wikidata!

 * Skills required: Swift for iOS; Kotlin for Android; Python and/or Wikidata Query Service for Wikidata queries and formatting
 * Get in touch: GitHub or email
 * Get the source code: GitHub
 * Read the contribution guidelines: iOS or Android
 * Check the recommended tasks: iOS or Android
 * Mentor(s): Andrew McAllister

 VideoCutTool

 A tool to edit the videos on Wikimedia Commons.

 * Skills required: React JS, Node JS.
 * Get in touch: #VideoCutTool in Zulip
 * Get the source code: See link in description in Phabricator
 * Read the documentation
 * Check the recommended tasks to work on: Phabricator
 * Mentor(s): Gopa Vasanth

 Are you a maintainer and want your project to be included in the list of software projects above? Find out more and join!

 Outreach programs and single tasks

 In addition to the recommended software projects above, there are more ways to choose a project or task to work on:

 Outreach programs

 Wikimedia offers internships in programs such as Google Summer of Code and Outreachy.

 Good first tasks

 There are many single tasks (across many software projects) that are suitable for newcomers.
 However, mentors may not be available for these tasks, and your proposed patches may not receive fast reviews.

 Communication tips

 Follow these tips to communicate effectively and get help from community members.

 Use Phabricator tasks effectively

 When you plan to work on a Phabricator task:

 * No need to ask for permission: You can work on unassigned tasks without asking someone to assign them to you. There is no authority who assigns tasks or who needs to be asked first.
 + If a task already has a recent patch in Gerrit, choose a different task to work on instead.
 + If an existing patch in Gerrit has not been merged and has not seen any changes for a long time, you could improve that existing patch, based on the feedback in Gerrit and in the task.
 * Do your research: When you consider working on a task, do research before you start coding. Look at the code, try to understand what it is supposed to do, read related documentation, and try to find the places where you need to make code changes.
 + In a Phabricator task, use the project tags in the side bar to find the code repository for the task.
 + If you have no idea at all how to fix the bug, consider finding an easier one first.
 * You do not need to announce your plans before you start working on a task, but you should communicate that you are working on the task.
 + When you start work, set yourself as task assignee by clicking Edit Task… in Phabricator, and set your Phabricator username in the Assigned To field. This communicates to others that you are working on it, so they don't duplicate work.
 + When your plans or interests change: If you are no longer working on a task, remove yourself as the assignee of the task. This tells others that they can work on the task, and they won't expect you to still work on it.
 * Follow Phabricator etiquette.
 + In Phabricator tasks, discuss only specific questions about the topic of that task. Don't use Phabricator to ask general questions, like how to set up a development environment or how to fix problems with Gerrit.

 Compose good questions

 * Don't ask to ask...just ask!.
 * Be specific and provide context: Instead of simply asking "Can you give me more info?", "Please guide me", or "Please tell me how to start", include the following information in your question:
 + What are you trying to achieve?
 + What have you already tried? Copy and paste your commands and their output (if not too long) instead of paraphrasing in your own words.
 + What have you found out already during your research? Include links to code, documentation, or other resources you already consulted.
 * Use specific titles and subject lines in your communication. "Proposal draft" or "Need help" is not specific.
 * Keep conversations readable: When you reply in Zulip, in Phabricator tasks, or on mailing lists, only quote sections of previous comments that are relevant to your response. If you quote a complete previous comment, it makes threads hard to read.

 Follow communication policies and best practices

 Before you send or post your question:

 * Read and follow the code of conduct for Wikimedia technical spaces.
 * Use Inclusive language: Instead of using terms that assume a gender identity (like "guys", "madam", or "sir") use the name of the person instead.

 Ask in the right place

 * Ask in public: Do not send private messages if your conversation topic is not secret. Private messages don't help others.
 * Ask and discuss in the best place:
 + In Phabricator tasks, discuss only specific questions about the topic of that task.
 + Ask general technical questions, like how to set up a development environment or how to fix problems with Gerrit, in the places listed on Communication.
 + If you take part in an outreach program, then Zulip is for discussing questions about the outreach programs themselves.

 Be patient

 After you post your question:

 * Do not ask people for code review in a separate message. People receive Gerrit and Phabricator notifications and will respond when they can.
 * When seeking input and comments, especially during weekends and holidays, you may need to wait until business hours resume. On chat channels like IRC: if nobody answers, try again at a different time; don't just give up!
 * If you don't get an answer even after waiting and being patient, consider if other Communication channels might be a better place to ask your question.

 Additional resources

 * Introduction to the Wikimedia Technical Ecosystem provides an overview of Wikimedia tech, focused on the major areas where developers can contribute.
 * How to contribute lists many more ways to contribute, including areas like documentation, testing, and more.
 * How to become a MediaWiki hacker: For developers who want to work on MediaWiki core or MediaWiki extensions.
 * Developer hub: More resources for established Wikimedia developers.
 * To ask your questions and to join general discussions, check the places listed on Communication.
 * Wikimedia tutorials: An index of tutorials that feature various languages, APIs, and frameworks in the Wikimedia technology stack.
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This page explains how to get started as a developer who wants to contribute to Wikimedia technical projects.
  Welcome!  
   Participants of the Wikimedia Hackathon 2019  
 Wikimedia's technical community always welcomes new contributors!
 Become part of a global community, and help make access to free knowledge easier for everyone!
  How to start contributing  
The following steps are a general outline of how to get started contributing:
 Learn the basics of how Wikimedia open source software projects work.
Read the Communication guidelines.
Set up accounts: Create a developer account. Depending on the type of contribution you want to make, you may also need to set up accounts in Phabricator, and set up Git and Gerrit.
 Choose a software project.
Choose and solve a task (write and test your code).
Submit your code changes for review. Follow the Guide to getting your code reviewed and submit a patch. 
The rest of this guide provides additional details about the process.
  Basics of how Wikimedia software projects work  
Wikimedia has software projects in many different areas. 
 The maintainers of each software project choose the infrastructure they prefer. In general, most software projects have: 
 a task tracking tool where software bugs and enhancement requests are reported, managed and discussed. Examples are Wikimedia Phabricator, GitHub, or Wikimedia GitLab.
a code repository where the source code can be "checked out" to everybody. Examples are Wikimedia Gerrit, GitHub, or Wikimedia GitLab.
a code review tool where proposed code changes ("patches") get discussed and improved. Examples are Wikimedia Git/Gerrit, GitHub, or GitLab. After your proposed patch is approved and merged into the code repository, your code changes become available to everybody.
general places for discussion of the software project and for help and support. Those places can be mailing lists, IRC chat channels, wiki pages, or other places. The exact places depend on each project. 
At any point, if you run into problems or need help, please ask. To ask good questions in the right places, follow the "communication tips".
  Contributing to software in MediaWiki  
Are you a user of a MediaWiki wiki looking to add a feature fix a bug in one?
Please see Finding software in MediaWiki to learn how to find the location of the software project that you are looking to contribute to.
  Overview of technical areas  
For an overview of Wikimedia technology and examples of the major areas where developers can contribute, visit  Introduction to the Wikimedia Technical Ecosystem.
  Choose a software project  
The following projects offer resources, mentorship, and are looking for new developers to contribute to them.
Choose one of the following projects and follow the project's documentation to set up your development environment, choose a task to work on, solve the task, and submit your code changes for review.
You are free to contribute to these projects or any others you are interested in related to Wikimedia.
Most can be found by searching for them on Phabricator or online.
 Are you a maintainer and want your project to be included in the list of software projects above? Find out more and join! 
  Outreach programs and single tasks  
In addition to the recommended software projects above, there are more ways to choose a project or task to work on:
	   Outreach programs 
	Wikimedia offers internships in programs such as Google Summer of Code and Outreachy. 
	   Good first tasks 
	There are many single tasks (across many software projects) that are suitable for newcomers.However, mentors may not be available for these tasks, and your proposed patches may not receive fast reviews.   
  Communication tips  
Follow these tips to communicate effectively and get help from community members.
Use Phabricator tasks effectively
When you plan to work on a Phabricator task:
  No need to ask for permission: You can work on unassigned tasks without asking someone to assign them to you. There is no authority who assigns tasks or who needs to be asked first.
 If a task already has a recent patch in Gerrit, choose a different task to work on instead.
If an existing patch in Gerrit has not been merged and has not seen any changes for a long time, you could improve that existing patch, based on the feedback in Gerrit and in the task.  
 Do your research: When you consider working on a task, do research before you start coding. Look at the code, try to understand what it is supposed to do, read related documentation, and try to find the places where you need to make code changes.
 In a Phabricator task, use the project tags in the side bar to find the code repository for the task.
If you have no idea at all how to fix the bug, consider finding an easier one first.  
You do not need to announce your plans before you start working on a task, but you should communicate that you are working on the task.
 When you start work, set yourself as task assignee by clicking Edit Task… in Phabricator, and set your Phabricator username in the Assigned To field. This communicates to others that you are working on it, so they don't duplicate work.
 When your plans or interests change: If you are no longer working on a task, remove yourself as the assignee of the task. This tells others that they can work on the task, and they won't expect you to still work on it.  
Follow Phabricator etiquette.
 In Phabricator tasks, discuss only specific questions about the topic of that task. Don't use Phabricator to ask general questions, like how to set up a development environment or how to fix problems with Gerrit.   
Compose good questions
  Don't ask to ask...just ask!.
 Be specific and provide context: Instead of simply asking "Can you give me more info?", "Please guide me", or "Please tell me how to start", include the following information in your question:
 What are you trying to achieve?
What have you already tried? Copy and paste your commands and their output (if not too long) instead of paraphrasing in your own words.
What have you found out already during your research? Include links to code, documentation, or other resources you already consulted.  
Use specific titles and subject lines in your communication. "Proposal draft" or "Need help" is not specific.
 Keep conversations readable: When you reply in Zulip, in Phabricator tasks, or on mailing lists, only quote sections of previous comments that are relevant to your response. If you quote a complete previous comment, it makes threads hard to read. 
Follow communication policies and best practices
Before you send or post your question:
 Read and follow the code of conduct for Wikimedia technical spaces.
 Use Inclusive language: Instead of using terms that assume a gender identity (like "guys", "madam", or "sir") use the name of the person instead. 
Ask in the right place
  Ask in public: Do not send private messages if your conversation topic is not secret. Private messages don't help others.
 Ask and discuss in the best place:
 In Phabricator tasks, discuss only specific questions about the topic of that task.
Ask general technical questions, like how to set up a development environment or how to fix problems with Gerrit, in the places listed on Communication.
If you take part in an outreach program, then Zulip is for discussing questions about the outreach programs themselves.   
Be patient
After you post your question:
 Do not ask people for code review in a separate message. People receive Gerrit and Phabricator notifications and will respond when they can.
When seeking input and comments, especially during weekends and holidays, you may need to wait until business hours resume. On chat channels like IRC: if nobody answers, try again at a different time; don't just give up!
If you don't get an answer even after waiting and being patient, consider if other Communication channels might be a better place to ask your question. 
  Additional resources  
   Introduction to the Wikimedia Technical Ecosystem provides an overview of Wikimedia tech, focused on the major areas where developers can contribute.
 How to contribute lists many more ways to contribute, including areas like documentation, testing, and more.
 How to become a MediaWiki hacker: For developers who want to work on MediaWiki core or MediaWiki extensions.
 Developer hub: More resources for established Wikimedia developers.
To ask your questions and to join general discussions, check the places listed on Communication.
 Wikimedia tutorials: An index of tutorials that feature various languages, APIs, and frameworks in the Wikimedia technology stack.
New Developers - MediaWiki
https://www.mediawiki.org/wiki/New_Developers
https://towardsdatascience.com/artificial-intelligence-d1e45efc99b4?gi=9112ab4402a0
Artificial Intelligence: a concise conceptual introduction | Towards Data Science
2023-07-20T17:49:24Z
Leandro Mineti
<html><body><div><article><div><div><div><h2>A concise conceptual introduction</h2><div><a href="https://medium.com/@leandromineti?source=post_page-----d1e45efc99b4--------------------------------"><div><p></p></div></a><a href="https://towardsdatascience.com/?source=post_page-----d1e45efc99b4--------------------------------"><div><p></p></div></a></div></div><p></p><figure><figcaption>Photo by <a href="https://unsplash.com/@tfrm2003?utm_source=unsplash&amp;utm_medium=referral&amp;utm_content=creditCopyText">Tomás M</a> on <a href="https://unsplash.com/s/photos/fractal?utm_source=unsplash&amp;utm_medium=referral&amp;utm_content=creditCopyText">Unsplash</a>.</figcaption></figure><p></p><div><p>To talk about artificial intelligence, we have to start by having a reasonable definition of intelligence. In his recent paper ‘<a href="https://arxiv.org/abs/1911.01547"><em>On the measure of intelligence</em></a><em>.’</em>, Chollet describes two different definitions of intelligence dominating the literature:</p><ul><li><strong>Intelligence as a collection of task-specific skills</strong>: emphasizing the capacity to achieve goals.</li><li><strong>Intelligence as a general learning ability</strong>: emphasizing generality and adaptation.</li></ul><p>Assuming either definition, intelligence appears as a property in many natural systems. Life forms present intelligence in various ways, and the challenging task of describing and explaining this phenomenon is at the heart of the so-called Cognitive Sciences. Other than that, since its <a href="https://en.wikipedia.org/wiki/Dartmouth_workshop">founding conference</a> in 1956, the longstanding human effort to build intelligent machines has been labeled by the term Artificial Intelligence (AI). Right from the start, the main ideas on how to make intelligent artificial systems gravitated around two approaches:</p><ul><li><strong>Learning from experts</strong>: focusing on methods to distill knowledge into sets of rules or other explicit representations and loading those descriptions into machines. It is common to refer to methods in this tradition as <a href="https://en.wikipedia.org/wiki/Symbolic_artificial_intelligence">symbolic AI</a>.</li><li><strong>Learning from data</strong>: focusing on teaching machines by example. This core idea of allowing computers to learn directly from data is expressed by the umbrella term naming this paradigm: <a href="https://en.wikipedia.org/wiki/Machine_learning">machine learning</a>.</li></ul><p>Due to technical challenges and limited success on the symbolic front, many such methods fell into disuse, leading this paradigm to be commonly referred to as Good Old-Fashioned AI (GOFAI). Besides, the growing availability of computing power and data over the last decades drove machine learning to the forefront of AI research. If someone is talking about AI today, it is probably talking about machine learning.</p><p>It is crucial to notice that when machine learning appeared as a research field, the ‘learning from data’ approach was already the subject of another discipline: statistics. This overlap between statistics and machine learning has generated some debate over the years, and a good reference to start a discussion on the issue is Breiman’s paper ‘<a href="https://projecteuclid.org/euclid.ss/1009213726"><em>Statistical modeling: the two cultures</em></a><em>.’</em>. In a nutshell, the arguments go as follows:</p><ul><li><strong>Statistics</strong>: models data by assuming a stochastic model and estimating its parameters. Goodness-of-fit tests and residual examination assess the model quality.</li><li><strong>Machine learning</strong>: models data by assuming the model is complex and unknown. Its predictive power on a hold-out dataset assesses the quality of a model, e.g., cross-validation.</li></ul><p>Due to the technical nuances of the various solutions proposed by both traditions, it is hard to classify every technique as pertaining to one or another approach. Perhaps it is more useful to acknowledge these ‘two cultures’ as two opposing extremes of a spectrum, where the tools proposed by each tradition are laid down in the continuum between inference-centric and prediction-centric methods.</p><p>Now, having this background in mind, let’s move on to the complexities of machine learning solutions. Even if we concentrate the discussion about AI on machine learning, navigating the rich terminology surrounding the field is still no easy task. When discussing such a system, I find it useful to think of every machine-learning solution as consisting of five somewhat independent abstraction layers.</p></div></div><div><h2>Five layers of a machine learning solution</h2><figure><figcaption>The five overlapping abstraction layers on a machine learning solution.</figcaption></figure><h2>Technology</h2><figure><figcaption>Every solution depends on computational infrastructure.</figcaption></figure><ul><li><strong>Storage</strong>: depends on the dataset size, data type, required latency, etc.</li><li><strong>Computing</strong>: depends on required processing units, e.g., CPUs and GPUs, and if the processing is centralized or distributed.</li><li><strong>Development</strong>: depends on team expertise, toolset maturity, etc.</li></ul><p>Besides, like any other computational system, the decisions on each topic will have to consider other issues, such as budget limits, scalability, and maintainability. This layer has many options, ranging from a small system where data sits in your hard drive and is treated on a local Jupyter Notebook to massive pipelines on multi-cloud environments.</p><h2>Data</h2><figure><figcaption>Tables, texts, or images form the most common datasets.</figcaption></figure><p>It may seem obvious, but it’s worth stating: all machine learning solutions depend on data. Knowing which kind of data will be treated by the system will allow the system designer to make informed decisions about adequate modeling techniques to achieve the desired results. When talking about data, the concerns are usually about:</p><ul><li><strong>Data type</strong>: the way information is presented to the system. It may be on tables, texts, images, sounds, etc. Each data type presents unique challenges for which specific tools and methods are available.</li><li><strong>Dataset size</strong>: the amount of available data will affect decisions both on the technology and the model layer. Some models thrive on lots of data, while others are adequate for small datasets.</li><li><strong>Dependence</strong>: knowing if each data point in the dataset is independent or if some sort of dependence structure exists, e.g., time series and graphs, makes a big difference when choosing an adequate modeling technique.</li></ul><h2>Model</h2><figure><figcaption>There are many options when it comes to choosing the model.</figcaption></figure><p>Choosing a model is selecting the space of functions, or the hypothesis set, in which we will search for the best fitting model. Characterizing the previous layers will already inform this decision in some ways, deep learning models, for example, may require bigger datasets and specialized hardware to train. Additionally, there are particular characteristics that are central to this layer:</p><ul><li><strong>Capability</strong>: if the model can generate new instances of its learning data elements, it is called a <a href="https://en.wikipedia.org/wiki/Generative_artificial_intelligence">generative model</a>; if creates estimates based on its inputs, it is called a <a href="https://en.wikipedia.org/wiki/Discriminative_model">discriminative model</a>.</li><li><strong>Interpretability</strong>: the need to explain its prediction or the relations of the variables within the model is a critical aspect of the model choice.</li></ul><p>The direct assessment of the coefficients on a linear model or the thresholds on a decision tree can give us information about the relationship between the variables on the dataset. Other models, such as a Random Forest or deep neural networks, are hard to assess directly and may need additional <a href="https://github.com/slundberg/shap">tools</a> to get some insight into their inner workings.</p><h2>Method</h2><figure><figcaption>The three major approaches to machine learning.</figcaption></figure><p>The method, or learning approach, defines how data is used to search for a good model. It will heavily depend on the type of problems we are solving: clustering, classification, regression, control, etc. Most expositions about this aspect of machine learning tend to highlight three major approaches:</p><ul><li><strong>Unsupervised learning</strong>: where we do not have a particular target variable. The usual method to tackle segmentation and association tasks.</li><li><strong>Supervised learning</strong>: where we have a particular target variable. The usual method to tackle classification and regression problems.</li><li><strong>Reinforcement learning</strong>: where an agent learns how to achieve a goal by directly interacting with an environment.</li></ul><p>Although the learning approach characterization may seem a mere formality, it is a crucial definition of a machine learning system design. Specifying an adequate learning approach for a given problem will guide all the model training setup, including its assessment methods, learning metrics, and expected results.</p><p>It is worth keeping in mind that those three are not the only approaches available. Still, once you clearly understand their characteristics, it will be easier to understand other learning variations, such as <a href="https://en.wikipedia.org/wiki/Weak_supervision">semi-supervised</a>, <a href="https://en.wikipedia.org/wiki/Online_machine_learning">online</a>, <a href="https://en.wikipedia.org/wiki/Adversarial_machine_learning">adversarial</a>, etc.</p><h2>Application</h2><figure><figcaption>Each application solves a particular problem.</figcaption></figure><p>Applications are designed to solve problems, regardless of the underlying technique. The application is the final product of the machine learning system design. Some <a href="https://deepindex.org/">well-known applications</a> relying on machine learning nowadays are recommender systems, loan classifiers, anomaly detectors, and autonomous vehicles.</p><p>It is important to remember that virtually any of those applications could be built using hard-coded rules. Keeping this in mind is a reality check on the necessity of using machine learning techniques on a given solution. Software engineering has a lot of complexities by itself; relying on machine learning to build an application adds yet another layer of complexity that can lead to a significant increase in the <a href="https://papers.nips.cc/paper/5656-hidden-technical-debt-in-machine-learning-systems.pdf">technical debt</a> backlog.</p><h2>Conclusion</h2><p>Artificial intelligence is a complex research field, and having a clear overall picture is very useful, if not needed, for people dealing with this technology. The next time you face an application built using machine learning, try disentangling each abstraction layer to understand the designer’s choices in each one; it may improve your understanding of it. Finally, I hope this conceptual introduction may work as a simple map helping you navigate this vast field. For those wondering how to dig deeper into the subject, when in doubt, I always go back to Russell and Norvig’s excellent ‘<em>Artificial Intelligence: a modern approach.</em>’.</p></div></div></article></div></body></html>
A concise conceptual introduction                   Photo by Tomás M on Unsplash.     To talk about artificial intelligence, we have to start by having a reasonable definition of intelligence. In his recent paper ‘ On the measure of intelligence  .’, Chollet describes two different definitions of intelligence dominating the literature:   Intelligence as a collection of task-specific skills: emphasizing the capacity to achieve goals.  Intelligence as a general learning ability: emphasizing generality and adaptation.  Assuming either definition, intelligence appears as a property in many natural systems. Life forms present intelligence in various ways, and the challenging task of describing and explaining this phenomenon is at the heart of the so-called Cognitive Sciences. Other than that, since its founding conference in 1956, the longstanding human effort to build intelligent machines has been labeled by the term Artificial Intelligence (AI). Right from the start, the main ideas on how to make intelligent artificial systems gravitated around two approaches:   Learning from experts: focusing on methods to distill knowledge into sets of rules or other explicit representations and loading those descriptions into machines. It is common to refer to methods in this tradition as symbolic AI.  Learning from data: focusing on teaching machines by example. This core idea of allowing computers to learn directly from data is expressed by the umbrella term naming this paradigm: machine learning.  Due to technical challenges and limited success on the symbolic front, many such methods fell into disuse, leading this paradigm to be commonly referred to as Good Old-Fashioned AI (GOFAI). Besides, the growing availability of computing power and data over the last decades drove machine learning to the forefront of AI research. If someone is talking about AI today, it is probably talking about machine learning. It is crucial to notice that when machine learning appeared as a research field, the ‘learning from data’ approach was already the subject of another discipline: statistics. This overlap between statistics and machine learning has generated some debate over the years, and a good reference to start a discussion on the issue is Breiman’s paper ‘ Statistical modeling: the two cultures  .’. In a nutshell, the arguments go as follows:   Statistics: models data by assuming a stochastic model and estimating its parameters. Goodness-of-fit tests and residual examination assess the model quality.  Machine learning: models data by assuming the model is complex and unknown. Its predictive power on a hold-out dataset assesses the quality of a model, e.g., cross-validation.  Due to the technical nuances of the various solutions proposed by both traditions, it is hard to classify every technique as pertaining to one or another approach. Perhaps it is more useful to acknowledge these ‘two cultures’ as two opposing extremes of a spectrum, where the tools proposed by each tradition are laid down in the continuum between inference-centric and prediction-centric methods. Now, having this background in mind, let’s move on to the complexities of machine learning solutions. Even if we concentrate the discussion about AI on machine learning, navigating the rich terminology surrounding the field is still no easy task. When discussing such a system, I find it useful to think of every machine-learning solution as consisting of five somewhat independent abstraction layers.    Five layers of a machine learning solution  The five overlapping abstraction layers on a machine learning solution.  Technology  Every solution depends on computational infrastructure.    Storage: depends on the dataset size, data type, required latency, etc.  Computing: depends on required processing units, e.g., CPUs and GPUs, and if the processing is centralized or distributed.  Development: depends on team expertise, toolset maturity, etc.  Besides, like any other computational system, the decisions on each topic will have to consider other issues, such as budget limits, scalability, and maintainability. This layer has many options, ranging from a small system where data sits in your hard drive and is treated on a local Jupyter Notebook to massive pipelines on multi-cloud environments. Data  Tables, texts, or images form the most common datasets.  It may seem obvious, but it’s worth stating: all machine learning solutions depend on data. Knowing which kind of data will be treated by the system will allow the system designer to make informed decisions about adequate modeling techniques to achieve the desired results. When talking about data, the concerns are usually about:   Data type: the way information is presented to the system. It may be on tables, texts, images, sounds, etc. Each data type presents unique challenges for which specific tools and methods are available.  Dataset size: the amount of available data will affect decisions both on the technology and the model layer. Some models thrive on lots of data, while others are adequate for small datasets.  Dependence: knowing if each data point in the dataset is independent or if some sort of dependence structure exists, e.g., time series and graphs, makes a big difference when choosing an adequate modeling technique.  Model  There are many options when it comes to choosing the model.  Choosing a model is selecting the space of functions, or the hypothesis set, in which we will search for the best fitting model. Characterizing the previous layers will already inform this decision in some ways, deep learning models, for example, may require bigger datasets and specialized hardware to train. Additionally, there are particular characteristics that are central to this layer:   Capability: if the model can generate new instances of its learning data elements, it is called a generative model; if creates estimates based on its inputs, it is called a discriminative model.  Interpretability: the need to explain its prediction or the relations of the variables within the model is a critical aspect of the model choice.  The direct assessment of the coefficients on a linear model or the thresholds on a decision tree can give us information about the relationship between the variables on the dataset. Other models, such as a Random Forest or deep neural networks, are hard to assess directly and may need additional tools to get some insight into their inner workings. Method  The three major approaches to machine learning.  The method, or learning approach, defines how data is used to search for a good model. It will heavily depend on the type of problems we are solving: clustering, classification, regression, control, etc. Most expositions about this aspect of machine learning tend to highlight three major approaches:   Unsupervised learning: where we do not have a particular target variable. The usual method to tackle segmentation and association tasks.  Supervised learning: where we have a particular target variable. The usual method to tackle classification and regression problems.  Reinforcement learning: where an agent learns how to achieve a goal by directly interacting with an environment.  Although the learning approach characterization may seem a mere formality, it is a crucial definition of a machine learning system design. Specifying an adequate learning approach for a given problem will guide all the model training setup, including its assessment methods, learning metrics, and expected results. It is worth keeping in mind that those three are not the only approaches available. Still, once you clearly understand their characteristics, it will be easier to understand other learning variations, such as semi-supervised, online, adversarial, etc. Application  Each application solves a particular problem.  Applications are designed to solve problems, regardless of the underlying technique. The application is the final product of the machine learning system design. Some well-known applications relying on machine learning nowadays are recommender systems, loan classifiers, anomaly detectors, and autonomous vehicles. It is important to remember that virtually any of those applications could be built using hard-coded rules. Keeping this in mind is a reality check on the necessity of using machine learning techniques on a given solution. Software engineering has a lot of complexities by itself; relying on machine learning to build an application adds yet another layer of complexity that can lead to a significant increase in the technical debt backlog. Conclusion Artificial intelligence is a complex research field, and having a clear overall picture is very useful, if not needed, for people dealing with this technology. The next time you face an application built using machine learning, try disentangling each abstraction layer to understand the designer’s choices in each one; it may improve your understanding of it. Finally, I hope this conceptual introduction may work as a simple map helping you navigate this vast field. For those wondering how to dig deeper into the subject, when in doubt, I always go back to Russell and Norvig’s excellent ‘Artificial Intelligence: a modern approach.’.
Artificial Intelligence: a concise conceptual introduction | Towards Data Science
https://towardsdatascience.com/artificial-intelligence-d1e45efc99b4?gi=63a63ace5871
https://www.brainstobytes.com/ml-concepts-supervised-learning/
ML Concepts: Supervised learning
2019-11-26
Juan Orozco Villalobos
<div><div>
	<p>Supervised learning is perhaps the most common form of machine learning task in use nowadays.</p>
<p>This form of learning makes use of a labeled training dataset to create a model that predicts a target of interest. If this line makes absolutely no sense to you, don't worry. After reading this article you will have a clear understanding of supervised learning and its two most popular applications: regression and classification.</p>
<h2>Training machines with examples</h2>
<p>Supervised learning is a process in which you teach a machine to predict a particular result by feeding it examples 'with the right answers'.</p>
<p>The first thing you need to know is what are you trying to predict. You might want to create a program that classifies pet photos as <em>dog photos</em> or <em>cat photos</em>, or a program that predicts the prices of houses in different districts in Sydney, Australia.</p>
<p>After deciding the variable you are trying to predict (your <strong>target</strong>), it's time to gather data examples from the real world and <em>label them</em>. In our first example, we would start gathering photos with dogs and photos with cats and tagging them with the right category. This photo of a puppy is a dog photo, that photo of a cat playing with a laser is a cat photo, and so on for every example.</p>
<p>Before the training stage, you will set aside a percentage of your training set to test the performance of your models. Afterwards, you will feed your labeled examples into an algorithm that will learn to generalize a relationship between the inputs (the photos) and the targets (dog/cat), producing a model you can use to classify fresh images it has never seen before. In this context, this is what <em>training</em> means: teaching a machine to perform actions learned from training data.</p>
<p>You can evaluate how well the model performs on your training set, the one you put aside before training. If the results are satisfying, you can deploy the model into production and use it to solve the original problem. The following diagram shows a high-level view of the supervised learning process.</p>
<p></p>
<p>This is an example of a classification task.</p>
<p><strong>Classification</strong> and <strong>regression</strong> are the most common applications of supervised learning. If you are interested in a career in machine learning you will likely spend most of your time creating these types of models, so let's take a look at them.</p>
<h2>Classifying the world</h2>
<p>A classifier is a model that tells you the <strong>class</strong>(category) an instance of your data belongs to. In the previous example, our instances were photos of pets, and the classes were <em>cat photos</em> and <em>dog photos</em>.</p>
<p>The training set for classification tasks is usually a collection of instances (individual instances of the phenomenon you are trying to model) with a <em>label</em> that specifies the class they belong to.</p>
<p>Classifiers can be further classified ( ͡° ͜ʖ ͡° ) into different subtypes depending on the number of target classes (binary or multiclass) and how many categories an instance can belong to at the same time (single-label and multi-label), let's take a look at those.</p>
<h4>Binary classifiers</h4>
<p>A binary classifier is a model that classifies examples into two possible classes. Classifiers are capable of telling you if an email is either <strong>spam</strong> or <strong>not spam</strong>, if a photo of a face is <strong>happy</strong> or <strong>sad</strong> or if a substance is <strong>harmless</strong> or <strong>dangerous</strong>.</p>
<p>The most common setup for binary classification is to have a positive class (<em>class</em>) and a negative class (<em>not-class</em>). In this sense, you can re-define the previous examples as spam/not-spam, happy/not-happy and dangerous/not-dangerous.</p>
<p>Some types of binary classifiers don't just tell you a result, but they also provide you a probability that the instance you are classifying belongs to the predicted class.</p>
<p>Binary classifiers are some of the most studied and used models in machine learning, and many other models build on top of them (like some forms of multiclass classifiers).</p>
<p></p>
<h4>Multiclass classifiers</h4>
<p>As you might imagine from the title, a multiclass classifier is a model that classifies instances into many categories. Like in the previous case you can get the results as the probability of belonging to a particular class.</p>
<p>It's important to note that there is a difference depending on the number of classes an instance can belong to at the same time.</p>
<p>If the classes are mutually exclusive (an object can only belong to one class at a time) you are building a <strong>single-label multiclass classifier</strong>. If an instance can belong to more than 1 class at the same time then you need a <strong>multi-label classifier</strong>.</p>
<p>Depending on the particular scenario, your choice of algorithms and evaluation methods will differ.</p>
<p></p>
<p></p>
<h2>Regression</h2>
<p>The goal of a regression model is to predict a continuous value. The training set for a regression problem is usually a collection of instances with the associated numeric value you are trying to predict.</p>
<p>The following are some examples of regression problems</p>
<ul>
<li>Predict the price of houses in Amsterdam given the size of the house (in square meters), the year the house was built, the average income of the area in which the house is located, the number of bedrooms and the color of the mailbox.</li>
<li>Predict a person's likelihood developing diabetes given the height, weight, number of cigarettes smoked per day, average caloric intake, average hours of physical activity per week and amount of carbs consumed per day.</li>
<li>Predict the stock price of a company one year from now based on the number of Disney films released last year, the color of underwear the CEO wears with more frequency and the title of his/her aunt's favorite song.</li>
</ul>
<p>Regression tasks are extremely common in machine learning. If you decide to pursue a career in data science or ML engineering, many of the models you'll build are likely aimed to solve regression problems.</p>
<p></p>
<h2>The core assumption of supervised learning</h2>
<p>Ok, now you have an idea of what supervised learning is and how the process works. In brief, you collect a lot of data relevant to the problem you are trying to solve and label it with the <em>correct answers</em>, or the expected result your model is trying to predict. Then, all this training data is fed into an algorithm that will generate a model that maps the inputs into classes(classification) or values(regression).</p>
<p>For this process to work, the information contained in the training set needs to have enough <strong>predictive power</strong> for the algorithm to find a correlation between the two sets.</p>
<p>For example, if you want to predict the likelihood a given person has to develop diabetes, you might want data like the BMI, genetic predisposition and dietary habits. All 3 with powerful correlation with the variable you are trying to find (likelihood to develop a disease, in this case). Other data, like favorite film, shoe size, and favorite headphone brand has less predictive power for this particular target, so it makes little sense to add it to the training set.</p>
<p>Sometimes, the data gathered doesn't provide enough information to build a model that performs well, in this scenario you need to reformulate the problem or find data with better quality.</p>
<p>Supervised learning is a huge topic with lots of important concepts. The goal of this article was to present a high-level view of the topic. Hopefully, by now you have a better understanding of supervised learning, and we will be prepared to dig deeper in more elaborate topics in future articles.</p>
<p>Thank you for reading!</p>
<h2>What to do next</h2>
<ul>
<li>Share this article with friends and colleagues. Thank you for helping me reach people who might find this information useful.</li>
<li>This article is based on Data Science for Business: What You Need to Know about Data Mining and Data-Analytic Thinking. This and other very helpful books can be found in the <a href="https://www.brainstobytes.com/recommended-books/">recommended reading list</a>.</li>
<li>Send me an email with questions, comments or suggestions (it's in the <a href="https://www.brainstobytes.com/about">About Me page</a>)</li>
</ul>
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 ML Concepts: Supervised learning

 By Juan Orozco Villalobos • November 26, 2019

 Supervised learning is perhaps the most common form of machine learning task in use nowadays.

 This form of learning makes use of a labeled training dataset to create a model that predicts a target of interest. If this line makes absolutely no sense to you, don't worry. After reading this article you will have a clear understanding of supervised learning and its two most popular applications: regression and classification.

 Training machines with examples

 Supervised learning is a process in which you teach a machine to predict a particular result by feeding it examples 'with the right answers'.

 The first thing you need to know is what are you trying to predict. You might want to create a program that classifies pet photos as dog photos or cat photos, or a program that predicts the prices of houses in different districts in Sydney, Australia.

 After deciding the variable you are trying to predict (your target), it's time to gather data examples from the real world and label them. In our first example, we would start gathering photos with dogs and photos with cats and tagging them with the right category. This photo of a puppy is a dog photo, that photo of a cat playing with a laser is a cat photo, and so on for every example.

 Before the training stage, you will set aside a percentage of your training set to test the performance of your models. Afterwards, you will feed your labeled examples into an algorithm that will learn to generalize a relationship between the inputs (the photos) and the targets (dog/cat), producing a model you can use to classify fresh images it has never seen before. In this context, this is what training means: teaching a machine to perform actions learned from training data.

 You can evaluate how well the model performs on your training set, the one you put aside before training. If the results are satisfying, you can deploy the model into production and use it to solve the original problem. The following diagram shows a high-level view of the supervised learning process.

 This is an example of a classification task.

 Classification and regression are the most common applications of supervised learning. If you are interested in a career in machine learning you will likely spend most of your time creating these types of models, so let's take a look at them.

 Classifying the world

 A classifier is a model that tells you the class(category) an instance of your data belongs to. In the previous example, our instances were photos of pets, and the classes were cat photos and dog photos.

 The training set for classification tasks is usually a collection of instances (individual instances of the phenomenon you are trying to model) with a label that specifies the class they belong to.

 Classifiers can be further classified ( ͡° ͜ʖ ͡° ) into different subtypes depending on the number of target classes (binary or multiclass) and how many categories an instance can belong to at the same time (single-label and multi-label), let's take a look at those.

 Binary classifiers

 A binary classifier is a model that classifies examples into two possible classes. Classifiers are capable of telling you if an email is either spam or not spam, if a photo of a face is happy or sad or if a substance is harmless or dangerous.

 The most common setup for binary classification is to have a positive class (class) and a negative class (not-class). In this sense, you can re-define the previous examples as spam/not-spam, happy/not-happy and dangerous/not-dangerous.

 Some types of binary classifiers don't just tell you a result, but they also provide you a probability that the instance you are classifying belongs to the predicted class.

 Binary classifiers are some of the most studied and used models in machine learning, and many other models build on top of them (like some forms of multiclass classifiers).

 Multiclass classifiers

 As you might imagine from the title, a multiclass classifier is a model that classifies instances into many categories. Like in the previous case you can get the results as the probability of belonging to a particular class.

 It's important to note that there is a difference depending on the number of classes an instance can belong to at the same time.

 If the classes are mutually exclusive (an object can only belong to one class at a time) you are building a single-label multiclass classifier. If an instance can belong to more than 1 class at the same time then you need a multi-label classifier.

 Depending on the particular scenario, your choice of algorithms and evaluation methods will differ.

 Regression

 The goal of a regression model is to predict a continuous value. The training set for a regression problem is usually a collection of instances with the associated numeric value you are trying to predict.

 The following are some examples of regression problems

 * Predict the price of houses in Amsterdam given the size of the house (in square meters), the year the house was built, the average income of the area in which the house is located, the number of bedrooms and the color of the mailbox.
 * Predict a person's likelihood developing diabetes given the height, weight, number of cigarettes smoked per day, average caloric intake, average hours of physical activity per week and amount of carbs consumed per day.
 * Predict the stock price of a company one year from now based on the number of Disney films released last year, the color of underwear the CEO wears with more frequency and the title of his/her aunt's favorite song.

 Regression tasks are extremely common in machine learning. If you decide to pursue a career in data science or ML engineering, many of the models you'll build are likely aimed to solve regression problems.

 The core assumption of supervised learning

 Ok, now you have an idea of what supervised learning is and how the process works. In brief, you collect a lot of data relevant to the problem you are trying to solve and label it with the correct answers, or the expected result your model is trying to predict. Then, all this training data is fed into an algorithm that will generate a model that maps the inputs into classes(classification) or values(regression).

 For this process to work, the information contained in the training set needs to have enough predictive power for the algorithm to find a correlation between the two sets.

 For example, if you want to predict the likelihood a given person has to develop diabetes, you might want data like the BMI, genetic predisposition and dietary habits. All 3 with powerful correlation with the variable you are trying to find (likelihood to develop a disease, in this case). Other data, like favorite film, shoe size, and favorite headphone brand has less predictive power for this particular target, so it makes little sense to add it to the training set.

 Sometimes, the data gathered doesn't provide enough information to build a model that performs well, in this scenario you need to reformulate the problem or find data with better quality.

 Supervised learning is a huge topic with lots of important concepts. The goal of this article was to present a high-level view of the topic. Hopefully, by now you have a better understanding of supervised learning, and we will be prepared to dig deeper in more elaborate topics in future articles.

 Thank you for reading!

 What to do next

 * Share this article with friends and colleagues. Thank you for helping me reach people who might find this information useful.
 * This article is based on Data Science for Business: What You Need to Know about Data Mining and Data-Analytic Thinking. This and other very helpful books can be found in the recommended reading list.
 * Send me an email with questions, comments or suggestions (it's in the About Me page)
 Machine Learning & Data
 * 
 * 
 * 
 * 
 * 
 About Juan Orozco Villalobos
 Budapest, Hungary
 Hey there, I'm Juan. A programmer currently living in Budapest. I believe in well-engineered solutions, clean code and sharing knowledge. Thanks for reading, I hope you find my articles useful!
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 Copyright © 2023, BrainsToBytes. All right Reserved.
Supervised learning is perhaps the most common form of machine learning task in use nowadays.
This form of learning makes use of a labeled training dataset to create a model that predicts a target of interest. If this line makes absolutely no sense to you, don't worry. After reading this article you will have a clear understanding of supervised learning and its two most popular applications: regression and classification.
Training machines with examples
Supervised learning is a process in which you teach a machine to predict a particular result by feeding it examples 'with the right answers'.
The first thing you need to know is what are you trying to predict. You might want to create a program that classifies pet photos as dog photos or cat photos, or a program that predicts the prices of houses in different districts in Sydney, Australia.
After deciding the variable you are trying to predict (your target), it's time to gather data examples from the real world and label them. In our first example, we would start gathering photos with dogs and photos with cats and tagging them with the right category. This photo of a puppy is a dog photo, that photo of a cat playing with a laser is a cat photo, and so on for every example.
Before the training stage, you will set aside a percentage of your training set to test the performance of your models. Afterwards, you will feed your labeled examples into an algorithm that will learn to generalize a relationship between the inputs (the photos) and the targets (dog/cat), producing a model you can use to classify fresh images it has never seen before. In this context, this is what training means: teaching a machine to perform actions learned from training data.
You can evaluate how well the model performs on your training set, the one you put aside before training. If the results are satisfying, you can deploy the model into production and use it to solve the original problem. The following diagram shows a high-level view of the supervised learning process.
 
This is an example of a classification task.
 Classification and regression are the most common applications of supervised learning. If you are interested in a career in machine learning you will likely spend most of your time creating these types of models, so let's take a look at them.
Classifying the world
A classifier is a model that tells you the class(category) an instance of your data belongs to. In the previous example, our instances were photos of pets, and the classes were cat photos and dog photos.
The training set for classification tasks is usually a collection of instances (individual instances of the phenomenon you are trying to model) with a label that specifies the class they belong to.
Classifiers can be further classified ( ͡° ͜ʖ ͡° ) into different subtypes depending on the number of target classes (binary or multiclass) and how many categories an instance can belong to at the same time (single-label and multi-label), let's take a look at those.
Binary classifiers
A binary classifier is a model that classifies examples into two possible classes. Classifiers are capable of telling you if an email is either spam or not spam, if a photo of a face is happy or sad or if a substance is harmless or dangerous.
The most common setup for binary classification is to have a positive class (class) and a negative class (not-class). In this sense, you can re-define the previous examples as spam/not-spam, happy/not-happy and dangerous/not-dangerous.
Some types of binary classifiers don't just tell you a result, but they also provide you a probability that the instance you are classifying belongs to the predicted class.
Binary classifiers are some of the most studied and used models in machine learning, and many other models build on top of them (like some forms of multiclass classifiers).
 
Multiclass classifiers
As you might imagine from the title, a multiclass classifier is a model that classifies instances into many categories. Like in the previous case you can get the results as the probability of belonging to a particular class.
It's important to note that there is a difference depending on the number of classes an instance can belong to at the same time.
If the classes are mutually exclusive (an object can only belong to one class at a time) you are building a single-label multiclass classifier. If an instance can belong to more than 1 class at the same time then you need a multi-label classifier.
Depending on the particular scenario, your choice of algorithms and evaluation methods will differ.
 
 
Regression
The goal of a regression model is to predict a continuous value. The training set for a regression problem is usually a collection of instances with the associated numeric value you are trying to predict.
The following are some examples of regression problems
Predict the price of houses in Amsterdam given the size of the house (in square meters), the year the house was built, the average income of the area in which the house is located, the number of bedrooms and the color of the mailbox.
Predict a person's likelihood developing diabetes given the height, weight, number of cigarettes smoked per day, average caloric intake, average hours of physical activity per week and amount of carbs consumed per day.
Predict the stock price of a company one year from now based on the number of Disney films released last year, the color of underwear the CEO wears with more frequency and the title of his/her aunt's favorite song.
Regression tasks are extremely common in machine learning. If you decide to pursue a career in data science or ML engineering, many of the models you'll build are likely aimed to solve regression problems.
 
The core assumption of supervised learning
Ok, now you have an idea of what supervised learning is and how the process works. In brief, you collect a lot of data relevant to the problem you are trying to solve and label it with the correct answers, or the expected result your model is trying to predict. Then, all this training data is fed into an algorithm that will generate a model that maps the inputs into classes(classification) or values(regression).
For this process to work, the information contained in the training set needs to have enough predictive power for the algorithm to find a correlation between the two sets.
For example, if you want to predict the likelihood a given person has to develop diabetes, you might want data like the BMI, genetic predisposition and dietary habits. All 3 with powerful correlation with the variable you are trying to find (likelihood to develop a disease, in this case). Other data, like favorite film, shoe size, and favorite headphone brand has less predictive power for this particular target, so it makes little sense to add it to the training set.
Sometimes, the data gathered doesn't provide enough information to build a model that performs well, in this scenario you need to reformulate the problem or find data with better quality.
Supervised learning is a huge topic with lots of important concepts. The goal of this article was to present a high-level view of the topic. Hopefully, by now you have a better understanding of supervised learning, and we will be prepared to dig deeper in more elaborate topics in future articles.
Thank you for reading!
What to do next
Share this article with friends and colleagues. Thank you for helping me reach people who might find this information useful.
This article is based on Data Science for Business: What You Need to Know about Data Mining and Data-Analytic Thinking. This and other very helpful books can be found in the recommended reading list.
Send me an email with questions, comments or suggestions (it's in the About Me page)
ML Concepts: Supervised learning
https://www.brainstobytes.com/ml-concepts-supervised-learning/
https://www.tableau.com/learn/articles/blogs-about-machine-learning-artificial-intelligence
10 Great Machine Learning (ML) and Artificial Intelligence (AI) Blogs To Follow
2024-01-01
None
<div><div>
<main>
<section>
<article>
<div>
<section>
<article>
<p>Machine learning (ML) isn’t new. However, the field of big data is revitalizing the subject and more organizations are relying on ML models to scale their operations, support staff in working better and faster, to uncover hidden insights from data, or even confirm and challenge underlying assumptions. This is creating widespread interest in related topics with the C-suite, and across business lines and job roles, as enterprises embrace the value of <a href="https://www.tableau.com/data-insights/ai/what-is">artificial intelligence (AI)</a> and ML. To make a disruptive organizational impact, AI and ML need to be understood and trusted. By consulting these ML blogs from authoritative individuals and organizations that satisfy different skill levels, readers can increase their understanding and comfort level in these areas, get pressing questions answered, and connect with others who have experience using them to great benefit.</p>
</article>
</section>
<section>
<article>
<div>
<h3>1. <a href="https://openai.com/">OpenAI</a></h3>
<p><strong>OpenAI</strong> comes from industry experts who want to bring AI to the masses. It's linked to the non-profit research company OpenAI, co-chaired by Elon Musk and Sam Altman, and sponsored by companies such as Amazon Web Services, Microsoft, and Infosys who are trying to make AI accessible—hence the name. Contributors discuss their collective efforts to promote and advance AI technologies through long-term research. It’s a valuable resource for anyone interested in the future of AI.</p>
</div>
</article>
</section>
<section>
<article>
<div>
<h3>2. <a href="https://distill.pub/">Distill</a></h3>
<p><strong>Managed by:</strong> Shan Carter, Chris Olah, and Arvind Satyanarayan</p>
<p><strong>Distill</strong> concentrates on making ML and AI more accessible for readers. Traditional research can be difficult to consume, so Distill communicates ML research in appealing, interactive data visualizations. It acts as a neutral platform for multiple authors to publish together, and articles are peer-reviewed, appearing in Google Scholar. <strong>Distill</strong> is also registered with the Library of Congress and CrossRef.</p>
</div>
</article>
</section>
<section>
<article>
<div>
<h3>3. <a href="https://www.machinelearningisfun.com/">Machine Learning is Fun</a></h3>
<p><strong>Authored by</strong>: <a href="https://adamgeitgey.com/">Adam Geitgey</a></p>
<p><strong>Machine Learning is Fun</strong> is a valuable, introductory blog. It covers the tenets of ML through interactive tutorials and practical examples, which make it easier to see the useful applications to different businesses and industries. Author Adam Geitgey is a former software developer who now consults organizations on implementing machine learning. He believes ML is integral to the future of software and that developers should have a strong working knowledge, so he provides guides and techniques to help them develop and grow.</p>
</div>
</article>
</section>
<section>
<article>
<div>
<h3>4. <a href="https://machinelearningmastery.com/blog/">Machine Learning Mastery</a></h3>
<p><strong>Authored by:</strong> Jason Brownlee</p>
<p>A machine learning developer with several AI-related degrees, Jason intended his <strong>Machine Learning Mastery</strong> blog for new developers getting started in the field. He was once an amateur developer and wants to help others, imparting lessons learned during his professional journey and sharing the tools that helped him most. The blog, plus his email course and newsletter, accommodate any level of expertise.</p>
</div>
</article>
</section>
<section>
<article>
<div>
<h3>5. <a href="https://bair.berkeley.edu/blog/">The BAIR Blog</a></h3>
<p><strong>Managed by:</strong> <a href="https://bair.berkeley.edu/">Berkeley Artificial Intelligence Research</a></p>
<p>The artificial intelligence research department at UC Berkeley created this blog to convey research findings and important information about their AI-related work. Covering a spectrum of research—from natural language processing to robotics—grad students and faculty contribute content for both experts and the general population to consume.</p>
</div>
</article>
</section>
<section>
<article>
<div>
<p></p>
</div>
</article>
</section>
<section>
<article>
<div>
<h3>6. <a href="http://fastml.com/">FastML</a></h3>
<p><strong>Managed by:</strong> Zygmunt Zając</p>
<p><strong>FastML</strong> tackles interesting topics in machine learning with entertaining, easy to consume posts. It’s run by economist Zygmunt Zając, and is a go-to ML platform, tackling topics like overfitting, pointer networks, and chatbots, among others. If you’re frustrated by some of the existing ML papers that feel like you need a PhD in math to understand them, bookmark this blog.</p>
</div>
</article>
</section>
<section>
<article>
<div>
<h3>7. <a href="https://www.aitrends.com/">AI Trends</a></h3>
<p><strong>Managed by:</strong> <a href="https://www.cambridgeinnovationinstitute.com/">Cambridge Innovation Institute</a></p>
<p>This media channel delivers comprehensive coverage of the latest AI-related technology and business news. It’s designed to keep executives ahead of the curve with artificial intelligence and machine learning. <strong>AI Trends</strong> features interviews with and thought leadership pieces from top business leaders, as well as in-depth articles on the business of AI.</p>
</div>
</article>
</section>
<section>
<article>
<div>
<h3>8. <a href="https://aws.amazon.com/blogs/machine-learning/">AWS Machine Learning Blog</a></h3>
<p>Amazon is heavily involved in ML, using algorithms in nearly all areas of its business to create leads. Algorithms suggest relevant products for customers in search results, recommend products based on recent purchases, and optimize faster product distribution and shipping from warehouses to customers. The blog features projects and guides that reveal industry strides to readers and covers ML uses in Amazon Web Services technology. </p>
</div>
</article>
</section>
<section>
<article>
<div>
<h3>9. <a href="https://machinelearning.apple.com/">Apple Machine Learning Journal</a></h3>
<p>Apple’s advancements in voice recognition, predictive text, and autocorrect leveraged for Siri signal some of its machine learning work. And their newest iPhone features ML predominantly in its processor, performing trillions of operations per second; it’s ML in your hands. <strong>Apple Machine Learning Journal</strong> is a helpful look at how ML shapes their different technologies, and Apple engineers give perspective on how their work influences the transformation of ML. </p>
</div>
</article>
</section>
<section>
<article>
<div>
<h3>10. AI at Google</h3>
<p><strong>Related links:</strong> <a href="https://ai.google/research">Google AI Research Blog</a> and <a href="https://www.blog.google/technology/ai/">Google AI Technology Blog</a></p>
<p>Google helped revolutionize machine learning, so to see their level of ML research isn’t surprising. Machine learning and AI critically support how Google technology works—from their search algorithms that redefined web searches, to Google Maps influencing how we navigate destinations, and now their self-driving car is changing the auto industry. Google makes its work available through posts discussing their published research and how its technology is used by others to influence AI innovation.</p>
</div>
</article>
</section>
<section>
<article>
<div>
<p>With greater understanding or appreciation for ML and AI, it’s easier to dispel the myths that may leave doubt about their full potential and to responsibly apply these productive solutions. A Tableau blog post recently explored <a href="https://www.tableau.com/about/blog/2018/9/three-common-machine-learning-misconceptions-94278">three common machine learning misconceptions</a>—reviewing them will help you discern fact from fiction in all the industry noise. </p>
<div><p>For anyone ready to embrace these models and put them to work, Andrew Beers, CTO at Tableau Software, wrote about how to effectively and <a href="https://www.linkedin.com/pulse/reflection-responsibly-applying-ai-andrew-beers/">responsibly apply AI techniques</a> taking cues from brands such as Box, eBay, OpenTable, and Slack. And the rise of explainable AI (i.e. techniques in AI which can be trusted and easily understood) topped Tableau’s <a href="https://www.tableau.com/reports/business-intelligence-trends">2019 annual report of influential BI trends</a>, signaling that more organizations are putting these trained, data-driven models to use in how they operate and solve complex challenges.</p></div>
<hr/>
<p><em>Disclaimer: Tableau does not officially endorse any products, publications, or opinions therein listed on this webpage, and as such this page does not engage with any affiliate link programs. This article is intended purely for educational purposes and the above information about products and publications is made available so that readers can make informed decisions for themselves.</em>
</p></div>
</article>
</section>
</div>
</article>
</section>
</main>
</div></div>||||I||||___
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 10 Great Machine Learning (ML) and Artificial Intelligence (AI) Blogs To Follow

 Machine learning (ML) isn’t new. However, the field of big data is revitalizing the subject and more organizations are relying on ML models to scale their operations, support staff in working better and faster, to uncover hidden insights from data, or even confirm and challenge underlying assumptions. This is creating widespread interest in related topics with the C-suite, and across business lines and job roles, as enterprises embrace the value of artificial intelligence (AI) and ML. To make a disruptive organizational impact, AI and ML need to be understood and trusted. By consulting these ML blogs from authoritative individuals and organizations that satisfy different skill levels, readers can increase their understanding and comfort level in these areas, get pressing questions answered, and connect with others who have experience using them to great benefit.

 1. OpenAI

 OpenAI comes from industry experts who want to bring AI to the masses. It's linked to the non-profit research company OpenAI, co-chaired by Elon Musk and Sam Altman, and sponsored by companies such as Amazon Web Services, Microsoft, and Infosys who are trying to make AI accessible—hence the name. Contributors discuss their collective efforts to promote and advance AI technologies through long-term research. It’s a valuable resource for anyone interested in the future of AI.

 2. Distill

 Managed by: Shan Carter, Chris Olah, and Arvind Satyanarayan

 Distill concentrates on making ML and AI more accessible for readers. Traditional research can be difficult to consume, so Distill communicates ML research in appealing, interactive data visualizations. It acts as a neutral platform for multiple authors to publish together, and articles are peer-reviewed, appearing in Google Scholar. Distill is also registered with the Library of Congress and CrossRef.

 3. Machine Learning is Fun

 Authored by: Adam Geitgey

 Machine Learning is Fun is a valuable, introductory blog. It covers the tenets of ML through interactive tutorials and practical examples, which make it easier to see the useful applications to different businesses and industries. Author Adam Geitgey is a former software developer who now consults organizations on implementing machine learning. He believes ML is integral to the future of software and that developers should have a strong working knowledge, so he provides guides and techniques to help them develop and grow.

 4. Machine Learning Mastery

 Authored by: Jason Brownlee

 A machine learning developer with several AI-related degrees, Jason intended his Machine Learning Mastery blog for new developers getting started in the field. He was once an amateur developer and wants to help others, imparting lessons learned during his professional journey and sharing the tools that helped him most. The blog, plus his email course and newsletter, accommodate any level of expertise.

 5. The BAIR Blog

 Managed by: Berkeley Artificial Intelligence Research

 The artificial intelligence research department at UC Berkeley created this blog to convey research findings and important information about their AI-related work. Covering a spectrum of research—from natural language processing to robotics—grad students and faculty contribute content for both experts and the general population to consume.

 Create beautiful visualizations with your data.

 Try Tableau for free

 6. FastML

 Managed by: Zygmunt Zając

 FastML tackles interesting topics in machine learning with entertaining, easy to consume posts. It’s run by economist Zygmunt Zając, and is a go-to ML platform, tackling topics like overfitting, pointer networks, and chatbots, among others. If you’re frustrated by some of the existing ML papers that feel like you need a PhD in math to understand them, bookmark this blog.

 7. AI Trends

 Managed by: Cambridge Innovation Institute

 This media channel delivers comprehensive coverage of the latest AI-related technology and business news. It’s designed to keep executives ahead of the curve with artificial intelligence and machine learning. AI Trends features interviews with and thought leadership pieces from top business leaders, as well as in-depth articles on the business of AI.

 8. AWS Machine Learning Blog

 Amazon is heavily involved in ML, using algorithms in nearly all areas of its business to create leads. Algorithms suggest relevant products for customers in search results, recommend products based on recent purchases, and optimize faster product distribution and shipping from warehouses to customers. The blog features projects and guides that reveal industry strides to readers and covers ML uses in Amazon Web Services technology.

 9. Apple Machine Learning Journal

 Apple’s advancements in voice recognition, predictive text, and autocorrect leveraged for Siri signal some of its machine learning work. And their newest iPhone features ML predominantly in its processor, performing trillions of operations per second; it’s ML in your hands. Apple Machine Learning Journal is a helpful look at how ML shapes their different technologies, and Apple engineers give perspective on how their work influences the transformation of ML.

 10. AI at Google

 Related links: Google AI Research Blog and Google AI Technology Blog

 Google helped revolutionize machine learning, so to see their level of ML research isn’t surprising. Machine learning and AI critically support how Google technology works—from their search algorithms that redefined web searches, to Google Maps influencing how we navigate destinations, and now their self-driving car is changing the auto industry. Google makes its work available through posts discussing their published research and how its technology is used by others to influence AI innovation.

 With greater understanding or appreciation for ML and AI, it’s easier to dispel the myths that may leave doubt about their full potential and to responsibly apply these productive solutions. A Tableau blog post recently explored three common machine learning misconceptions—reviewing them will help you discern fact from fiction in all the industry noise.

 For anyone ready to embrace these models and put them to work, Andrew Beers, CTO at Tableau Software, wrote about how to effectively and responsibly apply AI techniques taking cues from brands such as Box, eBay, OpenTable, and Slack. And the rise of explainable AI (i.e. techniques in AI which can be trusted and easily understood) topped Tableau’s 2019 annual report of influential BI trends, signaling that more organizations are putting these trained, data-driven models to use in how they operate and solve complex challenges.


 Disclaimer: Tableau does not officially endorse any products, publications, or opinions therein listed on this webpage, and as such this page does not engage with any affiliate link programs. This article is intended purely for educational purposes and the above information about products and publications is made available so that readers can make informed decisions for themselves.

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Machine learning (ML) isn’t new. However, the field of big data is revitalizing the subject and more organizations are relying on ML models to scale their operations, support staff in working better and faster, to uncover hidden insights from data, or even confirm and challenge underlying assumptions. This is creating widespread interest in related topics with the C-suite, and across business lines and job roles, as enterprises embrace the value of artificial intelligence (AI) and ML. To make a disruptive organizational impact, AI and ML need to be understood and trusted. By consulting these ML blogs from authoritative individuals and organizations that satisfy different skill levels, readers can increase their understanding and comfort level in these areas, get pressing questions answered, and connect with others who have experience using them to great benefit.
1. OpenAI 
 OpenAI comes from industry experts who want to bring AI to the masses. It's linked to the non-profit research company OpenAI, co-chaired by Elon Musk and Sam Altman, and sponsored by companies such as Amazon Web Services, Microsoft, and Infosys who are trying to make AI accessible—hence the name. Contributors discuss their collective efforts to promote and advance AI technologies through long-term research. It’s a valuable resource for anyone interested in the future of AI.
2. Distill 
 Managed by: Shan Carter, Chris Olah, and Arvind Satyanarayan
 Distill concentrates on making ML and AI more accessible for readers. Traditional research can be difficult to consume, so Distill communicates ML research in appealing, interactive data visualizations. It acts as a neutral platform for multiple authors to publish together, and articles are peer-reviewed, appearing in Google Scholar. Distill is also registered with the Library of Congress and CrossRef.
3. Machine Learning is Fun 
 Authored by: Adam Geitgey 
 Machine Learning is Fun is a valuable, introductory blog. It covers the tenets of ML through interactive tutorials and practical examples, which make it easier to see the useful applications to different businesses and industries. Author Adam Geitgey is a former software developer who now consults organizations on implementing machine learning. He believes ML is integral to the future of software and that developers should have a strong working knowledge, so he provides guides and techniques to help them develop and grow.
4. Machine Learning Mastery 
 Authored by: Jason Brownlee
A machine learning developer with several AI-related degrees, Jason intended his Machine Learning Mastery blog for new developers getting started in the field. He was once an amateur developer and wants to help others, imparting lessons learned during his professional journey and sharing the tools that helped him most. The blog, plus his email course and newsletter, accommodate any level of expertise.
5. The BAIR Blog 
 Managed by: Berkeley Artificial Intelligence Research 
The artificial intelligence research department at UC Berkeley created this blog to convey research findings and important information about their AI-related work. Covering a spectrum of research—from natural language processing to robotics—grad students and faculty contribute content for both experts and the general population to consume.
 
6. FastML 
 Managed by: Zygmunt Zając
 FastML tackles interesting topics in machine learning with entertaining, easy to consume posts. It’s run by economist Zygmunt Zając, and is a go-to ML platform, tackling topics like overfitting, pointer networks, and chatbots, among others. If you’re frustrated by some of the existing ML papers that feel like you need a PhD in math to understand them, bookmark this blog.
7. AI Trends 
 Managed by: Cambridge Innovation Institute 
This media channel delivers comprehensive coverage of the latest AI-related technology and business news. It’s designed to keep executives ahead of the curve with artificial intelligence and machine learning. AI Trends features interviews with and thought leadership pieces from top business leaders, as well as in-depth articles on the business of AI.
8. AWS Machine Learning Blog 
Amazon is heavily involved in ML, using algorithms in nearly all areas of its business to create leads. Algorithms suggest relevant products for customers in search results, recommend products based on recent purchases, and optimize faster product distribution and shipping from warehouses to customers. The blog features projects and guides that reveal industry strides to readers and covers ML uses in Amazon Web Services technology. 
9. Apple Machine Learning Journal 
Apple’s advancements in voice recognition, predictive text, and autocorrect leveraged for Siri signal some of its machine learning work. And their newest iPhone features ML predominantly in its processor, performing trillions of operations per second; it’s ML in your hands. Apple Machine Learning Journal is a helpful look at how ML shapes their different technologies, and Apple engineers give perspective on how their work influences the transformation of ML. 
10. AI at Google
 Related links: Google AI Research Blog and Google AI Technology Blog 
Google helped revolutionize machine learning, so to see their level of ML research isn’t surprising. Machine learning and AI critically support how Google technology works—from their search algorithms that redefined web searches, to Google Maps influencing how we navigate destinations, and now their self-driving car is changing the auto industry. Google makes its work available through posts discussing their published research and how its technology is used by others to influence AI innovation.
With greater understanding or appreciation for ML and AI, it’s easier to dispel the myths that may leave doubt about their full potential and to responsibly apply these productive solutions. A Tableau blog post recently explored three common machine learning misconceptions—reviewing them will help you discern fact from fiction in all the industry noise. 
 For anyone ready to embrace these models and put them to work, Andrew Beers, CTO at Tableau Software, wrote about how to effectively and responsibly apply AI techniques taking cues from brands such as Box, eBay, OpenTable, and Slack. And the rise of explainable AI (i.e. techniques in AI which can be trusted and easily understood) topped Tableau’s 2019 annual report of influential BI trends, signaling that more organizations are putting these trained, data-driven models to use in how they operate and solve complex challenges. 
 Disclaimer: Tableau does not officially endorse any products, publications, or opinions therein listed on this webpage, and as such this page does not engage with any affiliate link programs. This article is intended purely for educational purposes and the above information about products and publications is made available so that readers can make informed decisions for themselves.
10 Great Machine Learning (ML) and Artificial Intelligence (AI) Blogs To Follow
https://www.tableau.com/learn/articles/blogs-about-machine-learning-artificial-intelligence
https://blog.ml.cmu.edu/
Machine Learning Blog | ML@CMU | Carnegie Mellon University
2023-01-13
Machine Learning Department; Carnegie Mellon University
<div><div>
 
 
 <p><a href="https://blog.ml.cmu.edu/2023/01/13/bottom-up-top-down-detection-transformers-for-open-vocabulary-object-detection/">
 
 </a>
 </p>
 
 
 
 
 <p>We perform open vocabulary detection of the objects mentioned in the sentence using both bottom-up and top-down feedback. Object detection is the fundamental computer vision task of finding all “objects” that are present in a visual scene. However, this raises the question, what is an object? Typically, this question is side-stepped by defining a vocabulary of categories and then training a model to detect instances of this vocabulary. This means that if “apple” is not in this vocabulary, the model…</p>
 
 
 <ul>
 <li>
</li>
 <li>
</li>
</ul> 
 <hr />
</div>||||I|||| Machine Learning Blog | ML@CMU | Carnegie Mellon University

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 computer vision machine learning Research

 Bottom-up Top-Down Detection Transformers For Open Vocabulary Object Detection

 by Ayush Jain / January 13, 2023

 We perform open vocabulary detection of the objects mentioned in the sentence using both bottom-up and top-down feedback. Object detection is the fundamental computer vision task of finding all “objects” that are present in a visual scene. However, this raises the question, what is an object? Typically, this question is side-stepped by defining a vocabulary of categories and then training a model to detect instances of this vocabulary. This means that if “apple” is not in this vocabulary, the model…

 * ♥ 30 3814
 * 
 + 
 + 
 + 
 + 
 + 
 machine learning Research

 Causal Confounds in Sequential Decision Making

 November 28, 2022

 A standard assumption in sequential decision making is that we observe everything required to make good decisions. In practice however, this isn’t always the case. We discuss two specific examples (temporally correlated noise (a) and unobserved contexts (c)) that have…

 * ♥ 73 8117
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 + 
 + 
 + 
 Research

 How do Authors’ Perceptions about their Papers Compare with Co-authors’ Perceptions and Peer-review Decisions?

 November 22, 2022

 Alina Beygelzimer, Yann N. Dauphin, Percy Liang, Jennifer Wortman Vaughan(NeurIPS 2021 Program Chairs) Charvi Rastogi, Ivan Stelmakh, Zhenyu Xue, Hal Daumé III, Emma Pierson, and Nihar B. Shah There is a considerable body of research on peer review. Within the…

 * ♥ 231 7702 3
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 automl deep learning machine learning Research

 Tackling Diverse Tasks with Neural Architecture Search

 October 14, 2022

 DASH searches for the optimal kernel size and dilation rate efficiently from a large set of options for each convolutional layer in a CNN backbone. The resulting model can achieve task-specific feature extraction and work as well as hand-designed expert…

 * ♥ 91 7260
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 computer vision deep learning machine learning Research

 Tracking Any Pixel in a Video

 September 9, 2022

 We upgrade pixels into PIPs: “Persistent Independent Particles”. With this representation, we track any pixel over time, and overcome visibility issues with a learned temporal prior. Motion estimation is a fundamental task of computer vision, with extremely broad applications. By…

 * ♥ 128 10817
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 machine learning Research

 Long-term Dynamics of Fairness Intervention in Connection Recommender Systems

 September 2, 2022

 Figure 1: Modeled recommendation cycle. We demonstrate how enforcing group-fairness in every recommendation slate separately does not necessarily promote equity in second order variables of interest like network size. Connection recommendation is at the heart of user experience in many…

 * ♥ 127 3076
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 machine learning reinforcement learning Research

 Recurrent Model-Free RL Can Be a Strong Baseline for Many POMDPs

 August 26, 2022

 Figure 1. Our implementation of recurrent model-free RL outperforms the on-policy version (PPO/A2C-GRU), and a recent model-based POMDP algorithm (VRM) on most tasks of a POMDP benchmark where VRM was evaluated in their paper. While algorithms for decision-making typically focus…

 * ♥ 133 3408
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 machine learning Research

 Galaxies on Graph Neural Networks

 August 19, 2022

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We perform open vocabulary detection of the objects mentioned in the sentence using both bottom-up and top-down feedback. Object detection is the fundamental computer vision task of finding all “objects” that are present in a visual scene. However, this raises the question, what is an object? Typically, this question is side-stepped by defining a vocabulary of categories and then training a model to detect instances of this vocabulary. This means that if “apple” is not in this vocabulary, the model…
Machine Learning Blog | ML@CMU | Carnegie Mellon University
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https://github-wiki-see.page/m/tobigithub/tensorflow-deep-learning/wiki/tf-links-blogs
tf links blogs - tobigithub/tensorflow-deep-learning GitHub Wiki
2017-11-30
None
<div><div>
<p>This page collects some of the recent interesting articles regarding the release of tensorflow.</p>
<p><h3>TF Links</h3><a href="#tf-links"></a></p>
<ul>
<li>
<p><a href="https://cloud.google.com/tpu/">Google Cloud TPU</a> - //May 2017// Google makes powerful cloud TPU available to researchers <a href="https://www.tensorflow.org/tfrc/">(1000 TPUs)</a> <a href="https://arstechnica.com/information-technology/2017/05/google-brings-45-teraflops-tensor-flow-processors-to-its-compute-cloud/">(Background)</a> and here is some hardware and performance info from Norman P. Jouppi <a href="https://www.nextplatform.com/2017/04/05/first-depth-look-googles-tpu-architecture/">(Background2)</a> <a href="https://arxiv.org/ftp/arxiv/papers/1704/1704.04760.pdf">(PDF)</a></p>
</li>
<li>
<p><a href="https://github.com/tensorflow/tensorflow/tree/master/tensorflow/contrib/slim">TF-Slim</a> - a simplified and lightweight package to train TF models (<a href="https://research.googleblog.com/2016/08/tf-slim-high-level-library-to-define.html">Google Blog</a>)</p>
</li>
<li>
<p><a href="https://cloudplatform.googleblog.com/2016/05/Google-supercharges-machine-learning-tasks-with-custom-chip.html">Tensorflow TPU</a> - a custom ASIC or application-specific integrated circuit, that is specifically designed for running TensorFlow very efficiently (CPU &lt;&gt; GPU &lt;&gt; FPGA &lt;&gt; ASIC) check performance per Watt (<a href="https://www.youtube.com/watch?v=ae97jo4wtis">Video</a>)</p>
</li>
<li>
<p><a href="https://github.com/tensorflow/models/tree/master/syntaxnet">Parsey McParseface and SyntaxNet</a> - a syntactic parser that can identify the constructs of English sentences (<a href="http://googleresearch.blogspot.fr/2016/05/announcing-syntaxnet-worlds-most.html">blog</a>)</p>
</li>
<li>
<p><a href="http://playground.tensorflow.org">TensorFlow PlayGround</a> - tinker with a Neural Network (it will eat <strong>your</strong> CPU) a really cool, visual and mind-bending software implementation</p>
</li>
</ul>
<p><h3>Links</h3><a href="#links"></a></p>
<ul>
<li>
<a href="http://www.wired.com/2015/11/googles-open-source-ai-tensorflow-signals-fast-changing-hardware-world/">Wired</a> - Tensorflow will change the world</li>
<li>
<a href="http://www.wired.com/2015/11/tensorflow-alone-will-not-revolutionize-ai/">Wired</a> - Tensorflow will actually not change the world</li>
<li>
<a href="http://www.bbc.com/news/technology-30290540">Stephen Hawking</a> - AI will kill us</li>
<li>
<a href="http://www.bbc.com/news/technology-31023741">Eric Horvitz</a> - AI will actually not kill us</li>
<li>
<a href="https://en.wikipedia.org/wiki/Three_Laws_of_Robotics">Isaac Asimov</a> - Three robotic laws will protect us</li>
<li>
<a href="https://gizmodo.com/5260042/asimovs-laws-of-robotics-are-total-bs">Daniel Wilson</a> - Three robotic laws will actually not protect us</li>
</ul>
<p><h3>Blogs</h3><a href="#blogs"></a></p>
<ul>
<li>
<a href="https://stratechery.com/2015/tensorflow-and-monetizing-intellectual-property/">Ben Thompson on TF</a> - Why did Alphabet give TensorFlow away?</li>
<li>
<a href="http://www.bloomberg.com/news/articles/2015-10-29/apple-s-secrecy-hurts-its-ai-software-development">Apple AI</a> - Why is Apple not contributing to Open AI software?</li>
<li>
<a href="http://arstechnica.com/information-technology/2015/12/facebooks-open-sourcing-of-ai-hardware-is-the-start-of-the-deep-learning-revolution/">Apple Big Sur</a> - Why is Apple contributing AI hardware designs and supports Torch AI?</li>
<li>
<a href="https://indico.io/blog/indico-tensorflow/">indico tf</a> - The indico Machine Learning Team’s Take on TensorFlow</li>
<li>
<a href="http://kivantium.hateblo.jp/entry/2015/11/18/233834">kivantium@hatena</a> - no idea, but looks convincing</li>
<li>
<a href="https://www.theguardian.com/society/2015/nov/19/pigeons-can-identify-cancerous-tissue-on-x-rays-study-finds">Pigeon AI</a> - Pigeons are smarter than most AI</li>
</ul>
<p><h3>Deep Learning and more</h3><a href="#deep-learning-and-more"></a></p>
<ul>
<li>
<a href="http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic-research/graham/">Ben Graham</a> - deep net convolution networks</li>
<li>
<a href="http://deeplearning.net/tutorial/">DL tutorials</a> - deep learning tutorials</li>
<li>
<a href="http://brage.bibsys.no/xmlui/bitstream/handle/11250/293860/15-00486-11%20Masteravhandling%20235135_1_1.pdf">MRI classification</a> - Automatic Classification of Alzheimer’s Disease from Structural MRI</li>
<li>
<a href="http://stanford.edu/~rezab/nips2014workshop/slides/jeff.pdf">Large Neural Nets</a> - Techniques and Systems for Training Large Neural Networks Quickly by Jeff Dean (Google Research)</li>
<li>
<a href="http://stats.stackexchange.com/questions/114385/what-is-the-difference-between-convolutional-neural-networks-restricted-boltzma">DL NNets explained</a> - Autoencoder, Restricted Boltzmann machine and Convolutional Neural Networks compared</li>
<li>
<a href="http://www.nature.com/nature/journal/v529/n7587/full/nature16961.html">AlphaGo</a> - Monte-Carlo tree search with deep neural networks from <a href="http://deepmind.com">DeepMind/Google</a>
</li>
<li>
<a href="https://www.ibm.com/blogs/research/2016/09/deep-learning-possible-embedded-systems-thanks-truenorth/">TrueNorth</a> - a fast and energy efficient real time CMOS chip for deep learning from IBM</li>
<li>
<a href="https://www.intelnervana.com/">Nervana</a> - Intels neural network specialty processor, an answer to NVIDIAs Volta GPU.</li>
</ul>
<p><h3>Deep learning systems</h3><a href="#deep-learning-systems"></a></p>
<ul>
<li>
<a href="http://torch.ch/">Torch</a> - scientific computing framework with machine learning support with additional modules from <a href="https://research.facebook.com/blog/879898285375829/fair-open-sources-deep-learning-modules-for-torch/">Facebook AI Research</a>
</li>
<li>
<a href="https://velesnet.ml/">Veles</a> - Distributed Deep Learning Platform by Samsung</li>
<li>
<a href="http://www.dmtk.io/">DMTK</a> - Distributed Machine Learning Toolkit by Microsoft</li>
<li>
<a href="https://www.cntk.ai/">CNTK</a> - Computational Network Toolkit by Microsoft</li>
<li>
<a href="https://developer.ibm.com/open/systemml/">SystemML</a> - SystemML using the Declarative Machine Learning (DML) by IBM</li>
<li>
<a href="https://github.com/baidu/Paddle">PaddlePaddle</a> - PaddlePaddle the PArallel Distributed Deep LEarning by Baidu</li>
<li>
<a href="https://caffe2.ai/">Caffe2</a> - Facebook supported Lightweight, Modular, and Scalable Deep Learning Framework using GPUs</li>
</ul>
</div></div>||||I|||| ⚠️ The indexable preview below may have rendering errors, broken links, and missing images. Please view the original page on GitHub.com and not this indexable preview if you intend to use this content.

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 tf links blogs - tobigithub/tensorflow-deep-learning GitHub Wiki

 This page collects some of the recent interesting articles regarding the release of tensorflow.

 TF Links

 * Google Cloud TPU - //May 2017// Google makes powerful cloud TPU available to researchers (1000 TPUs) (Background) and here is some hardware and performance info from Norman P. Jouppi (Background2) (PDF)

 * TF-Slim - a simplified and lightweight package to train TF models (Google Blog)

 * Tensorflow TPU - a custom ASIC or application-specific integrated circuit, that is specifically designed for running TensorFlow very efficiently (CPU <> GPU <> FPGA <> ASIC) check performance per Watt (Video)

 * Parsey McParseface and SyntaxNet - a syntactic parser that can identify the constructs of English sentences (blog)

 * TensorFlow PlayGround - tinker with a Neural Network (it will eat your CPU) a really cool, visual and mind-bending software implementation

 Links

 * Wired - Tensorflow will change the world
 * Wired - Tensorflow will actually not change the world
 * Stephen Hawking - AI will kill us
 * Eric Horvitz - AI will actually not kill us
 * Isaac Asimov - Three robotic laws will protect us
 * Daniel Wilson - Three robotic laws will actually not protect us

 Blogs

 * Ben Thompson on TF - Why did Alphabet give TensorFlow away?
 * Apple AI - Why is Apple not contributing to Open AI software?
 * Apple Big Sur - Why is Apple contributing AI hardware designs and supports Torch AI?
 * indico tf - The indico Machine Learning Team’s Take on TensorFlow
 * kivantium@hatena - no idea, but looks convincing
 * Pigeon AI - Pigeons are smarter than most AI

 Deep Learning and more

 * Ben Graham - deep net convolution networks
 * DL tutorials - deep learning tutorials
 * MRI classification - Automatic Classification of Alzheimer’s Disease from Structural MRI
 * Large Neural Nets - Techniques and Systems for Training Large Neural Networks Quickly by Jeff Dean (Google Research)
 * DL NNets explained - Autoencoder, Restricted Boltzmann machine and Convolutional Neural Networks compared
 * AlphaGo - Monte-Carlo tree search with deep neural networks from DeepMind/Google
 * TrueNorth - a fast and energy efficient real time CMOS chip for deep learning from IBM
 * Nervana - Intels neural network specialty processor, an answer to NVIDIAs Volta GPU.

 Deep learning systems

 * Torch - scientific computing framework with machine learning support with additional modules from Facebook AI Research
 * Veles - Distributed Deep Learning Platform by Samsung
 * DMTK - Distributed Machine Learning Toolkit by Microsoft
 * CNTK - Computational Network Toolkit by Microsoft
 * SystemML - SystemML using the Declarative Machine Learning (DML) by IBM
 * PaddlePaddle - PaddlePaddle the PArallel Distributed Deep LEarning by Baidu
 * Caffe2 - Facebook supported Lightweight, Modular, and Scalable Deep Learning Framework using GPUs

 ⚠️ **GitHub.com Fallback** ⚠️

 🗂️ Page Index for this GitHub Wiki

 ℹ️ About GitHub Wiki SEE, a search engine enabler for GitHub Wikis as GitHub blocks most GitHub Wikis from search engines.

This page collects some of the recent interesting articles regarding the release of tensorflow.
 TF Links   
 Google Cloud TPU - //May 2017// Google makes powerful cloud TPU available to researchers (1000 TPUs) (Background) and here is some hardware and performance info from Norman P. Jouppi (Background2) (PDF) 
 TF-Slim - a simplified and lightweight package to train TF models (Google Blog)
 Tensorflow TPU - a custom ASIC or application-specific integrated circuit, that is specifically designed for running TensorFlow very efficiently (CPU &lt;&gt; GPU &lt;&gt; FPGA &lt;&gt; ASIC) check performance per Watt (Video)
 Parsey McParseface and SyntaxNet - a syntactic parser that can identify the constructs of English sentences (blog)
 TensorFlow PlayGround - tinker with a Neural Network (it will eat your CPU) a really cool, visual and mind-bending software implementation
 Links   
Wired - Tensorflow will change the world
Wired - Tensorflow will actually not change the world
Stephen Hawking - AI will kill us
Eric Horvitz - AI will actually not kill us
Isaac Asimov - Three robotic laws will protect us
Daniel Wilson - Three robotic laws will actually not protect us
 Blogs   
Ben Thompson on TF - Why did Alphabet give TensorFlow away?
Apple AI - Why is Apple not contributing to Open AI software?
Apple Big Sur - Why is Apple contributing AI hardware designs and supports Torch AI?
indico tf - The indico Machine Learning Team’s Take on TensorFlow
kivantium@hatena - no idea, but looks convincing
Pigeon AI - Pigeons are smarter than most AI
 Deep Learning and more   
Ben Graham - deep net convolution networks
DL tutorials - deep learning tutorials
MRI classification - Automatic Classification of Alzheimer’s Disease from Structural MRI
Large Neural Nets - Techniques and Systems for Training Large Neural Networks Quickly by Jeff Dean (Google Research)
DL NNets explained - Autoencoder, Restricted Boltzmann machine and Convolutional Neural Networks compared
AlphaGo - Monte-Carlo tree search with deep neural networks from DeepMind/Google
TrueNorth - a fast and energy efficient real time CMOS chip for deep learning from IBM
Nervana - Intels neural network specialty processor, an answer to NVIDIAs Volta GPU.
 Deep learning systems   
Torch - scientific computing framework with machine learning support with additional modules from Facebook AI Research
Veles - Distributed Deep Learning Platform by Samsung
DMTK - Distributed Machine Learning Toolkit by Microsoft
CNTK - Computational Network Toolkit by Microsoft
SystemML - SystemML using the Declarative Machine Learning (DML) by IBM
PaddlePaddle - PaddlePaddle the PArallel Distributed Deep LEarning by Baidu
Caffe2 - Facebook supported Lightweight, Modular, and Scalable Deep Learning Framework using GPUs
tf links blogs - tobigithub/tensorflow-deep-learning GitHub Wiki
https://github-wiki-see.page/m/tobigithub/tensorflow-deep-learning/wiki/tf-links-blogs
https://www.datarobot.com/wiki/artificial-intelligence/
Artificial Intelligence (AI)
2018-03-29
None
<div><div>
	<h2>What is Artificial Intelligence (AI)?</h2>
<p>The emergence of artificial intelligence (AI) has played a key part in ushering in the Fourth Industrial Revolution. According to the World Economic Forum, “<a href="https://www.weforum.org/agenda/2016/01/the-fourth-industrial-revolution-what-it-means-and-how-to-respond/">it is disrupting almost every industry in every country</a>.”</p>
<blockquote>
<p>“We stand on the brink of a technological revolution that will fundamentally alter the way we live, work, and relate to one another. In its scale, scope, and complexity, the transformation will be unlike anything humankind has experienced before.” – <a href="https://www.weforum.org/agenda/authors/klaus-schwab">Klaus Schwab,</a> Founder and Executive Chairman, World Economic Forum Geneva</p>
</blockquote>
<p>Artificial intelligence is a conglomeration of concepts and technologies that means different things to different people – self-driving cars, robots that impersonate humans, machine learning, and more – and its applications are everywhere you look. The typical definition of AI looks something like this:</p>
<p></p>
<p>Source: <a href="https://www.kdnuggets.com/2017/07/rapidminer-ai-machine-learning-deep-learning.html">KDNuggets</a></p>
<p>Jeremy Achin, CEO of <a href="https://www.datarobot.com/">DataRobot</a>, defines AI more simply:</p>
<blockquote>
<p>“An AI is a computer system that is able to perform tasks that ordinarily require human intelligence. These artificial intelligence systems are powered by machine learning. Many of them are powered by machine learning, some of them are powered by specifically deep learning, some of them are powered by very boring things like just rules.”</p>
</blockquote>
<p>For a more in-depth explanation, watch Jeremy’s <a href="https://www.youtube.com/watch?v=ZChA63CpX5o">keynote</a> on the subject from the Japan AI Experience.</p>
<h2>Why is Artificial Intelligence Important?</h2>
<p>Artificial intelligence systems are critical for companies that wish to extract value from data by automating and optimizing processes or producing actionable <a href="https://www.datarobot.com/wiki/insights/">insights</a>. Artificial intelligence systems powered by <a href="https://www.datarobot.com/wiki/machine-learning/">machine learning</a> enable companies to leverage large amounts of available data to uncover insights and patterns that would be impossible for any one person to identify, enabling them to deliver more targeted, personalized communications, predict critical care events, identify likely fraudulent transactions, and <a href="https://www.datarobot.com/use-cases/">more</a>.</p>
<p><a href="https://hbr.org/cover-story/2017/07/the-business-of-artificial-intelligence">Harvard Business Review</a> gives key insight into how important AI is in today’s economic environment:</p>
<blockquote>
<p>“The effects of AI will be magnified in the coming decade, as manufacturing, retailing, transportation, finance, healthcare, law, advertising, insurance, entertainment, education, and virtually every other industry transform their core processes and business models to take advantage of machine learning.”</p>
</blockquote>
<p>Companies that fail to adopt <a href="https://www.datarobot.com/platform/on-premise-ai-cluster/">AI</a> and machine learning technologies are fated to be left behind:</p>
<ul>
<li>Global spending on AI will <a href="https://www.idc.com/getdoc.jsp?containerId=prUS43095417">grow 50% compounded annually</a> and will reach $57.6 billion by 2021.</li>
<li>Industries like retail, marketing, healthcare, fintech, insurance, and <a href="https://venturebeat.com/2017/10/25/6-industries-with-massive-potential-for-ai-integration/">more</a> will all stand to benefit from AI and machine learning.</li>
<li>Companies driven by insights from data will <a href="https://www.forrester.com/InsightsDriven+Businesses+Will+Take+12+Trillion+A+Year+By+2020/-/E-PRE9365">take $1.2 trillion a year</a> from non-insight driven companies by 2020.</li>
<li><a href="https://www2.deloitte.com/us/en/pages/deloitte-analytics/articles/cognitive-technology-adoption-survey.html">83%</a> of early adopters are already gaining value from AI and machine learning initiatives.</li>
<li>The <a href="https://www.gartner.com/newsroom/id/3837763">net gain in jobs</a> resulting from AI adoption will be over 5 million.</li>
</ul>
<h2>Artificial Intelligence + DataRobot</h2>
<p>DataRobot was founded on the belief that emerging AI and machine learning technologies should be available to all enterprises, regardless of size and resources. That’s why we invented <a href="https://www.datarobot.com/wiki/automated-machine-learning/">automated machine learning</a>, which allows users of all skill levels to easily and rapidly build and <a href="https://www.datarobot.com/wiki/machine-learning-model-deployment/">deploy</a> machine learning <a href="https://www.datarobot.com/wiki/model/">models</a>.</p>
<p>DataRobot believes in the <a href="https://www.datarobot.com/resources/aidemocratization/">democratization of AI</a>, and for that reason, we developed a <a href="https://www.datarobot.com/platform/">platform</a> to enable business users across organizations to gain actionable, practical insights that result in tangible business value. DataRobot makes the power of AI accessible to users throughout your business, helping your organization transform into an <a href="https://www.datarobot.com/success/ai-driven-enterprise/">AI-driven enterprise</a>.</p>
 
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 Artificial Intelligence (AI)

 What is Artificial Intelligence (AI)?

 The emergence of artificial intelligence (AI) has played a key part in ushering in the Fourth Industrial Revolution. According to the World Economic Forum, “it is disrupting almost every industry in every country.”

 “We stand on the brink of a technological revolution that will fundamentally alter the way we live, work, and relate to one another. In its scale, scope, and complexity, the transformation will be unlike anything humankind has experienced before.” – Klaus Schwab, Founder and Executive Chairman, World Economic Forum Geneva

 Artificial intelligence is a conglomeration of concepts and technologies that means different things to different people – self-driving cars, robots that impersonate humans, machine learning, and more – and its applications are everywhere you look. The typical definition of AI looks something like this:

 Source: KDNuggets

 Jeremy Achin, CEO of DataRobot, defines AI more simply:

 “An AI is a computer system that is able to perform tasks that ordinarily require human intelligence. These artificial intelligence systems are powered by machine learning. Many of them are powered by machine learning, some of them are powered by specifically deep learning, some of them are powered by very boring things like just rules.”

 For a more in-depth explanation, watch Jeremy’s keynote on the subject from the Japan AI Experience.

 Why is Artificial Intelligence Important?

 Artificial intelligence systems are critical for companies that wish to extract value from data by automating and optimizing processes or producing actionable insights. Artificial intelligence systems powered by machine learning enable companies to leverage large amounts of available data to uncover insights and patterns that would be impossible for any one person to identify, enabling them to deliver more targeted, personalized communications, predict critical care events, identify likely fraudulent transactions, and more.

 Harvard Business Review gives key insight into how important AI is in today’s economic environment:

 “The effects of AI will be magnified in the coming decade, as manufacturing, retailing, transportation, finance, healthcare, law, advertising, insurance, entertainment, education, and virtually every other industry transform their core processes and business models to take advantage of machine learning.”

 Companies that fail to adopt AI and machine learning technologies are fated to be left behind:

 * Global spending on AI will grow 50% compounded annually and will reach $57.6 billion by 2021.
 * Industries like retail, marketing, healthcare, fintech, insurance, and more will all stand to benefit from AI and machine learning.
 * Companies driven by insights from data will take $1.2 trillion a year from non-insight driven companies by 2020.
 * 83% of early adopters are already gaining value from AI and machine learning initiatives.
 * The net gain in jobs resulting from AI adoption will be over 5 million.

 Artificial Intelligence + DataRobot

 DataRobot was founded on the belief that emerging AI and machine learning technologies should be available to all enterprises, regardless of size and resources. That’s why we invented automated machine learning, which allows users of all skill levels to easily and rapidly build and deploy machine learning models.

 DataRobot believes in the democratization of AI, and for that reason, we developed a platform to enable business users across organizations to gain actionable, practical insights that result in tangible business value. DataRobot makes the power of AI accessible to users throughout your business, helping your organization transform into an AI-driven enterprise.

 Delivering ROI for your artificial intelligence initiatives
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 * Ebook: 10 Keys to AI Success in 2022
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 * White Paper: Democratizing AI for All: Transforming Your Operating Model to Support AI Adoption
 * A Guide to Human-Centered AI: Best Practices in Organizational Change and Customer Experience
 * DataRobot Documentation: Glossary
 Who Is DataRobot?
 DataRobot was founded in 2012 to democratize access to AI. Today, DataRobot is the AI leader, with a vision to deliver a unified platform for all users, all data types, and all environments to accelerate delivery of AI to production for every organization.
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What is Artificial Intelligence (AI)?
The emergence of artificial intelligence (AI) has played a key part in ushering in the Fourth Industrial Revolution. According to the World Economic Forum, “it is disrupting almost every industry in every country.”
“We stand on the brink of a technological revolution that will fundamentally alter the way we live, work, and relate to one another. In its scale, scope, and complexity, the transformation will be unlike anything humankind has experienced before.” – Klaus Schwab, Founder and Executive Chairman, World Economic Forum Geneva
Artificial intelligence is a conglomeration of concepts and technologies that means different things to different people – self-driving cars, robots that impersonate humans, machine learning, and more – and its applications are everywhere you look. The typical definition of AI looks something like this:
 
Source: KDNuggets 
Jeremy Achin, CEO of DataRobot, defines AI more simply:
“An AI is a computer system that is able to perform tasks that ordinarily require human intelligence. These artificial intelligence systems are powered by machine learning. Many of them are powered by machine learning, some of them are powered by specifically deep learning, some of them are powered by very boring things like just rules.”
For a more in-depth explanation, watch Jeremy’s keynote on the subject from the Japan AI Experience.
Why is Artificial Intelligence Important?
Artificial intelligence systems are critical for companies that wish to extract value from data by automating and optimizing processes or producing actionable insights. Artificial intelligence systems powered by machine learning enable companies to leverage large amounts of available data to uncover insights and patterns that would be impossible for any one person to identify, enabling them to deliver more targeted, personalized communications, predict critical care events, identify likely fraudulent transactions, and more.
 Harvard Business Review gives key insight into how important AI is in today’s economic environment:
“The effects of AI will be magnified in the coming decade, as manufacturing, retailing, transportation, finance, healthcare, law, advertising, insurance, entertainment, education, and virtually every other industry transform their core processes and business models to take advantage of machine learning.”
Companies that fail to adopt AI and machine learning technologies are fated to be left behind:
Global spending on AI will grow 50% compounded annually and will reach $57.6 billion by 2021.
Industries like retail, marketing, healthcare, fintech, insurance, and more will all stand to benefit from AI and machine learning.
Companies driven by insights from data will take $1.2 trillion a year from non-insight driven companies by 2020.
 83% of early adopters are already gaining value from AI and machine learning initiatives.
The net gain in jobs resulting from AI adoption will be over 5 million.
Artificial Intelligence + DataRobot
DataRobot was founded on the belief that emerging AI and machine learning technologies should be available to all enterprises, regardless of size and resources. That’s why we invented automated machine learning, which allows users of all skill levels to easily and rapidly build and deploy machine learning models.
DataRobot believes in the democratization of AI, and for that reason, we developed a platform to enable business users across organizations to gain actionable, practical insights that result in tangible business value. DataRobot makes the power of AI accessible to users throughout your business, helping your organization transform into an AI-driven enterprise.
Artificial Intelligence (AI)
https://www.datarobot.com/wiki/artificial-intelligence/