We also provide a novel explanation of base-rate neglect , the most well-documented deviation from Bayes ’ rule , by modelling it as a weight decay mechanism which increases entropy . Keywords : Neural-network ; Bayes ’ rule ; Bayesian learning and inference ; base-rate neglect ; weight decay ; entropy Introduction Bayesian models are becoming prominent across a wide range of problems in cognitive science including inductive learning ( Tenenbaum , Kemp , & Shafto , 2006 ) , language ac- quisition ( Chater & Manning , 2006 ) , and vision ( Yuille & Kersten , 2006 ) . While these Bayesian ideas provide compu- tation level models , it is beneficial , and sometimes necessary , to appeal to some implementation-level ( biological ) models to explain human behaviour . Batch Normalization is a commonly used trick to improve the training of deep neural networks . These neural networks use L2 regularization , also called weight decay , ostensibly to prevent overfitting . However , we show that L2 regularization has no regularizing effect when combined with normalization . For this behavior , the building of the navigation controller is done entirely online by the optimization of a zero-order Takagi-Sugeno fuzzy inference system ( FIS ) by a backpropagation-like algorithm . It is used to minimize a cost function that is made up of a quadratic error term and a weight decay term that prevents excessive growth of the parameters of the consequent part . The procedure is performed entirely online , but in two steps . In this paper , inspired from our previous algorithm , which was based on the theory of Tsallis statistical mechanics , we develop a new evolving stochastic learning algorithm for neural networks . The new algorithm combines deterministic and stochastic search steps by employing a different adaptive stepsize for each network weight , and applies a form of noise that is characterized by the nonextensive entropic index q , regulated by a weight decay term . The behavior of the learning algorithm can be made more stochastic or deterministic depending on the trade off between the temperature T and the q values . We study dropout and weight decay applied to deep networks with rectified linear units and the quadratic loss . We show how using dropout in this context can be viewed as adding a regularization penalty term that grows exponentially with the depth of the network when the more traditional weight decay penalty grows polynomially . We then show how this difference affects the inductive bias of algorithms using one regularizer or the other : we describe a random source of data that dropout is unwilling to fit , but that is compatible with the inductive bias of weight decay . This provides a counterpoint to the suggestion that dropout discourages co-adaptation of weights . We also show that the dropout penalty can grow exponentially in the depth of the network while the weight-decay penalty remains essentially linear , and that dropout is insensitive to various re-scalings of the input features , outputs , and network weights . This last insensitivity implies that there are no isolated local minima of the dropout training criterion . A new weight decaying technique for neural network training is introduced . The proposed technique utilizes genetic algorithms in conjunction with a local optimization method to restrict the weights of the neural network in some range with desired generalization capabilities . While there are several dimensions to this problem , in this paper we study the problem of accurately categorizing/classifying the coupons . We propose and evaluate four different techniques for categorizing the coupons namely , word-based model , n-gram-based model , externally weighing model , weight decaying model which take advantage of known machine learning algorithms . We evaluate these techniques and they achieve high accuracies in the range of 73.1 % to 93.2 % . An iterative top-down approach is proposed for delamination segmentation based on grayscale morphological reconstruction . A weight-decay function was used to regularize the reconstruction for regional maxima extraction . The mean and coefficient of variation of temperature gradient estimated from delamination boundaries were used for discrimination . To apply the proposed method to general convolutional neural networks , the effects of batch normalization layers are also considered . By utilizing residual-learning-like reparameterization and a special weight decay loss , the trade-off between source and target performance is effectively controlled . The proposed method exhibits state-of-the-art performance in various continual learning scenarios . 2 . Mathematical explanation of the success of the above rate schedule : a rigorous proof that it is equivalent to the standard setting of BN + SGD + StandardRate Tuning + Weight Decay + Momentum . This equivalence holds for other normalization layers as well , Group Normalization , LayerNormalization , Instance Norm , etc . This approach allows balancing between the training error and norm of network weight vectors , which are the two objective functions of the multi-objective optimization problem . The method is applied to classification and regression problems and compared with Weight Decay ( WD ) , Support Vector Machines ( SVMs ) and standard Backpropagation ( BP ) . It is shown that the systematic procedure for training proposed results on good generalization neural models , and outperforms traditional methods . Our algorithm immediately detects new trends in the drifting sensor data stream and follows them . SenClu powerfully uses a light- weighted decaying technique that gives lower influence to old data . As sensor data are usually noisy , our algorithm is also outlier-aware . and . Typically ensured by the objective or a weight decay term . The next theorem has been proved in the seminal paper of Borkar 1997 . We address assumption ( A4 ) with weight decay in two ways : ( I ) Weight decay avoids problems with a discriminator that is region - wise constant and , therefore , does not have a locally stable generator . If the generator is perfect , then the discriminator is 0.5 everywhere . We tried many optimizers . We initially tried with Adam , that gave an accuracy of 74 % on Rank 1 on Market1501 dataset , then we introduced weight decay that helped us achieve higher accuracy . We then tried SGD with Cyclical Learning Rate scheduler , we were able to achieve much higher accuracy . COCO - Stuff experiments were trained only for 30 epochs , which however approximately matches the number of iterations on Cityscapes due to the considerably larger dataset size . For optimization , we use stochastic gradient descent with momentum and weight decay . For training data augmentation , we apply random horizontal flipping ( with prob . ) and random scaling selected from - before cropping the actual patches . Compression rates of more than an order of magnitude were demonstrated in [ 11 ] without sacrificing accuracy . In the same spirit hash functions were exploited in [ 5 ] . Early approaches to compression include biased weight decay [ 12 ] and [ 14 , 24 ] , which prunes the network based on the Hessian of the loss function . Recently , various combinations of clustering with representation learning have been proposed . The main advantage of the method is that it can remove not only the redundant nodes , but also some redundant weights of the surviving nodes . As a comparison , the L1 regularization ( Lasso ) is mainly designed for removing the redundant weights , and it is not very good at removing the redundant nodes . And the group Lasso can remove the redundant nodes , but not any weight of the surviving nodes . In this paper , we propose a regularization framework for the LSTD algorithm that overcomes these difficulties . In particular , we focus on the case of l1 regularization , which is robust to irrelevant features and also serves as a method for feature selection . Although the l1 regularized LSTD solution can not be expressed as a convex optimization problem , we present an algorithm similar to the Least Angle Regression ( LARS ) algorithm that can efficiently compute the optimal solution . The L0 regularizer measures the parameter sparsity directly and is invariant to the scaling of parameter values , but it can not provide useful gradients , and therefore requires complex optimization techniques . The L1 regularizer is almost everywhere differentiable and can be easily optimized with gradient descent . Yet it is not scale-invariant , causing the same shrinking rate to all parameters , which is inefficient in increasing sparsity . For the ill-posed fluorescent molecular tomography ( FMT ) inverse problem , the L1 regularization can protect the high-frequency information like edges while effectively reduce the image noise . However , the state-of-the-art L1 regularization-based algorithms for FMT reconstruction are expensive in memory , especially for large-scale problems . An efficient L1 regularization-based reconstruction algorithm based on nonlinear conjugate gradient with restarted strategy is proposed to increase the computational speed with low memory consumption . To address this issue , in this work we have presented a new approach for software defect prediction by combining genetic algorithm optimization process for feature subspace reduction and deep belief network for pattern learning . Deep belief networks are further improved by applying L1-regularization scheme resulting in better learning process by reducing the overfitting error . This combined model is implemented on SPIE lab software defect database . Driver gene selection is crucial to understand the heterogeneous system of cancer . To identity cancer driver genes , various statistical strategies have been proposed , especially the L1-type regularization methods have drawn a large amount of attention . However , the statistical approaches have been developed purely from algorithmic and statistical point , and the existing studies have applied the statistical approaches to genomic data analysis without consideration of biological knowledge . In GSR-NCR , the local sparsity and nonlocal self-similarity of images is simultaneously considered in a unified framework . Different from the previous methods based on sparsity-promoting convex regularization , we extend the non-convex weighted Lp ( 0 < p < 1 ) penalty function on group sparse coefficients of the data matrix , rather than conventional L1-based regularization . To reduce the computational complexity , instead of learning the dictionary with a high computational complexity from natural images , we learn the principle component analysis ( PCA ) based dictionary for each group . In this paper , we will propose two types of tolerant fuzzy c-means clustering with regularization terms . One is L2-regularization term and the other is L1-regularization one for tolerance vector . Introducing a concept of clusterwise tolerance , we have proposed tolerant fuzzy c-means clustering from the viewpoint of handling data more flexibly . This algorithm minimizes an objective function of the form φ(Bu ) + 1/2||FpSu - f||2 , where φ is the regularization term which may be nonsmooth . In image reconstruction , the φ term corresponds to total variation smoothing and/or L1 regularization term . The least square term 1/2||FpSu - f||2 is the fidelity term . We initialize weights using the initialization described in and accordingly ( row -) normalize input feature vectors . On the random graph datasets , we use a hidden layer size of 32 units and omit regularization ( i.e. neither dropout nor L2 regularization ) . subsection : Baselines In this case , the feature of text is a 1 , 720 dimensional vector . Dropout [ reference ] ) with the keep rate 0.75 and L2 regularization are performed to avoid overfitting . For the generator , we adopt LSTM [ reference ] as the architectures of MANAGER and WORKER to capture the sequence context information . subsubsection : Training We use categorical cross - entropy along with L2 - regularization as the measure of loss ( ) during training : where is the number of samples / dialogues , is the number of utterances in sample , is the probability distribution of emotion labels for utterance of dialogue , is the expected class label of utterance of dialogue , is the L2 - regularizer weight , and is the set of trainable parameters where We used stochastic gradient descent based Adam optimizer to train our network . Hyperparameters are optimized using grid search ( values are added to the supplementary material ) . We used mini - batch stochastic gradient decent and empirically found it effective to use a gradient clipping method with growing clipping values for the different tasks ; concretely , we employed the simple function : , where is the number of bi - LSTM layers involved in each task , and is the maximum value . We applied our successive regularization to our model , along with L2 - norm regularization and dropout dropout2014ver . More details are summarized in the supplemental material . section : D. Performance Comparison The LR and FM models are trained with L2 norm regularization , while FNN , CCPM and PNNs are trained with dropout . By default , we set dropout rate at 0.5 on network hidden layers , which is proved effective in Figure 2 . subsection : Regularization We use L2 norm regularization on the convolutional kernel parameters with a weight of . We also use the spatial dropout with a rate of after the initial encoder convolution . subsection : Regularization For regularization , we employ two commonly used techniques : dropout and L2 weight regularization . We apply dropout to prevent co - adaptation . textabstractWe consider a data assimilation problem for imperfect models . We propose a novel shadowing-based data assimilation method that takes model error into account following the Levenberg-Marquardt regularization approach . We illuminate how the proposed shadowing-based method is related to the weak constraint 4DVar method both analytically and numerically . The inversion scheme takes the form of an integral equation , which is discretized by means of the method of moments . The measured data are then inverted by means of the conjugate gradient ( CG ) fast Fourier transform algorithm , which incorporates Levenberg-Marquardt regularization and adaptive preconditioning schemes . The reconstruction of the flaw based on simulated as well as measured data , along with some of the salient features of the newly developed CG algorithm are presented . > To do this , we propose a method for jointly learning the structure and parameters of conditional random fields , formulating these tasks as a convex optimization problem . We consider block-L1 regularization for each set of features associated with an edge , and formalize an efficient projection method to find the globally optimal penalized maximum likelihood solution . We perform extensive numerical experiments comparing the presented method with related methods that approach the structure learning problem differently . Topology elements among the modeling cues are recovered by the Binary Space Partitioning ( BSP ) technique . The regularity of the building rooftop model is achieved by an implicit regularization process in the framework of Minimum Description Length ( MDL ) combined with Hypothesize and Test ( HAT ) . The parameters governing the MDL optimization are automatically estimated based on Min-Max optimization and Entropy-based weighting method . The diffractive filter converts spectral information to a spatial code on the sensor pixels . Following a calibration step , this code can be inverted via regularization-based linear algebra to compute the multispectral image . We experimentally demonstrated spectral resolution of 9.6 nm within the visible band ( 430–718 nm ) . To address this problem , we propose a novel nonconvex structure matrix decomposition model , where using a nonconvex surrogate ( i.e. , the l1 norm of logistic function ) on the singular values of a matrix to approximate the rank function . In addition , our model contains two structural regularizations : a group sparsity induced norm regularization to explore the relationship between each superpixel , making salient object highlighted consistently , and a Laplacian regularization to increase the distance between salient regions and non-salient regions in feature space . Finally , high-level priors are integrated to our model . However , this method is empirical and implements a global regularization parameter over all uterine sites , which is sub-optimal for EMMI given the severe eccentricity of body-uterus geometry . To address this limitation , we developed a spatial-dependent ( SP ) regularization method that considers both body-uterus eccentricity and EMG noise . We used electrical signals simulated with spherical and realistic geometry models to compare the reconstruction accuracy of the SP method to those of the CRESO and the L-Curve methods . The aim of this paper is to propose new regularization and filtering techniques for dense and sparse vector fields , and to focus on their application to non-rigid registration . Indeed , most of the regularization energies used in non-rigid registration operate independently on each coordinate of the transformation . However , SMR does not consider the local geometry of image samples , and it assumes that the training samples should exactly fit a linear model or a strict binary label matrix by left and right regression matrices . In order to enlarge margins between different classes and preserve the intrinsic geometry structure of samples in the transformed space , we will propose dynamic graph regularization and label relaxation-based SMR ( abbreviated as DGRLR-SMR ) method for two-dimensional supervised feature selection . First , the label relaxation SMR is established by relaxing the strict binary label matrix into a slack variable matrix via a nonnegative label relaxation matrix by the $ \varepsilon $ -dragging technique . In this paper , we investigate the origin of this ill-conditioning and the way in which it influences the resulting filters . Two data-driven subspace regularization approaches are proposed , and those are shown to outperform a regularization approach used in recent literature . The comparison of the methods is based on ground truth data that are recorded in-vivo . A number of techniques have been proposed in literature to address this problem . In this paper we propose a simple technique called fraternal dropout that takes advantage of dropout to achieve this goal . Specifically , we propose to train two identical copies of an RNN ( that share parameters ) with different dropout masks while minimizing the difference between their ( pre-softmax ) predictions . Their method uses the same dropout mask at each timestep . fraternal proposed fraternal dropout , which minimizes the differences between outputs from different dropout masks to be invariant to the dropout mask . DBLP :
We also provide a novel explanation of base-rate neglect , the most well-documented deviation from Bayes ’ rule , by modelling it as a weight decay mechanism which increases entropy . Keywords : Neural-network ; Bayes ’ rule ; Bayesian learning and inference ; base-rate neglect ; weight decay ; entropy Introduction Bayesian models are becoming prominent across a wide range of problems in cognitive science including inductive learning ( Tenenbaum , Kemp , & Shafto , 2006 ) , language ac- quisition ( Chater & Manning , 2006 ) , and vision ( Yuille & Kersten , 2006 ) . While these Bayesian ideas provide compu- tation level models , it is beneficial , and sometimes necessary , to appeal to some implementation-level ( biological ) models to explain human behaviour .
Batch Normalization is a commonly used trick to improve the training of deep neural networks . These neural networks use L2 regularization , also called weight decay , ostensibly to prevent overfitting . However , we show that L2 regularization has no regularizing effect when combined with normalization .
For this behavior , the building of the navigation controller is done entirely online by the optimization of a zero-order Takagi-Sugeno fuzzy inference system ( FIS ) by a backpropagation-like algorithm . It is used to minimize a cost function that is made up of a quadratic error term and a weight decay term that prevents excessive growth of the parameters of the consequent part . The procedure is performed entirely online , but in two steps .
In this paper , inspired from our previous algorithm , which was based on the theory of Tsallis statistical mechanics , we develop a new evolving stochastic learning algorithm for neural networks . The new algorithm combines deterministic and stochastic search steps by employing a different adaptive stepsize for each network weight , and applies a form of noise that is characterized by the nonextensive entropic index q , regulated by a weight decay term . The behavior of the learning algorithm can be made more stochastic or deterministic depending on the trade off between the temperature T and the q values .
We study dropout and weight decay applied to deep networks with rectified linear units and the quadratic loss . We show how using dropout in this context can be viewed as adding a regularization penalty term that grows exponentially with the depth of the network when the more traditional weight decay penalty grows polynomially . We then show how this difference affects the inductive bias of algorithms using one regularizer or the other : we describe a random source of data that dropout is unwilling to fit , but that is compatible with the inductive bias of weight decay .
This provides a counterpoint to the suggestion that dropout discourages co-adaptation of weights . We also show that the dropout penalty can grow exponentially in the depth of the network while the weight-decay penalty remains essentially linear , and that dropout is insensitive to various re-scalings of the input features , outputs , and network weights . This last insensitivity implies that there are no isolated local minima of the dropout training criterion .
A new weight decaying technique for neural network training is introduced . The proposed technique utilizes genetic algorithms in conjunction with a local optimization method to restrict the weights of the neural network in some range with desired generalization capabilities .
While there are several dimensions to this problem , in this paper we study the problem of accurately categorizing/classifying the coupons . We propose and evaluate four different techniques for categorizing the coupons namely , word-based model , n-gram-based model , externally weighing model , weight decaying model which take advantage of known machine learning algorithms . We evaluate these techniques and they achieve high accuracies in the range of 73.1 % to 93.2 % .
An iterative top-down approach is proposed for delamination segmentation based on grayscale morphological reconstruction . A weight-decay function was used to regularize the reconstruction for regional maxima extraction . The mean and coefficient of variation of temperature gradient estimated from delamination boundaries were used for discrimination .
To apply the proposed method to general convolutional neural networks , the effects of batch normalization layers are also considered . By utilizing residual-learning-like reparameterization and a special weight decay loss , the trade-off between source and target performance is effectively controlled . The proposed method exhibits state-of-the-art performance in various continual learning scenarios .
2 . Mathematical explanation of the success of the above rate schedule : a rigorous proof that it is equivalent to the standard setting of BN + SGD + StandardRate Tuning + Weight Decay + Momentum . This equivalence holds for other normalization layers as well , Group Normalization , LayerNormalization , Instance Norm , etc .
This approach allows balancing between the training error and norm of network weight vectors , which are the two objective functions of the multi-objective optimization problem . The method is applied to classification and regression problems and compared with Weight Decay ( WD ) , Support Vector Machines ( SVMs ) and standard Backpropagation ( BP ) . It is shown that the systematic procedure for training proposed results on good generalization neural models , and outperforms traditional methods .
Our algorithm immediately detects new trends in the drifting sensor data stream and follows them . SenClu powerfully uses a light- weighted decaying technique that gives lower influence to old data . As sensor data are usually noisy , our algorithm is also outlier-aware .
and . Typically ensured by the objective or a weight decay term . The next theorem has been proved in the seminal paper of Borkar 1997 .
We address assumption ( A4 ) with weight decay in two ways : ( I ) Weight decay avoids problems with a discriminator that is region - wise constant and , therefore , does not have a locally stable generator . If the generator is perfect , then the discriminator is 0.5 everywhere .
We tried many optimizers . We initially tried with Adam , that gave an accuracy of 74 % on Rank 1 on Market1501 dataset , then we introduced weight decay that helped us achieve higher accuracy . We then tried SGD with Cyclical Learning Rate scheduler , we were able to achieve much higher accuracy .
COCO - Stuff experiments were trained only for 30 epochs , which however approximately matches the number of iterations on Cityscapes due to the considerably larger dataset size . For optimization , we use stochastic gradient descent with momentum and weight decay . For training data augmentation , we apply random horizontal flipping ( with prob . ) and random scaling selected from - before cropping the actual patches .
Compression rates of more than an order of magnitude were demonstrated in [ 11 ] without sacrificing accuracy . In the same spirit hash functions were exploited in [ 5 ] . Early approaches to compression include biased weight decay [ 12 ] and [ 14 , 24 ] , which prunes the network based on the Hessian of the loss function . Recently , various combinations of clustering with representation learning have been proposed .
The main advantage of the method is that it can remove not only the redundant nodes , but also some redundant weights of the surviving nodes . As a comparison , the L1 regularization ( Lasso ) is mainly designed for removing the redundant weights , and it is not very good at removing the redundant nodes . And the group Lasso can remove the redundant nodes , but not any weight of the surviving nodes .
In this paper , we propose a regularization framework for the LSTD algorithm that overcomes these difficulties . In particular , we focus on the case of l1 regularization , which is robust to irrelevant features and also serves as a method for feature selection . Although the l1 regularized LSTD solution can not be expressed as a convex optimization problem , we present an algorithm similar to the Least Angle Regression ( LARS ) algorithm that can efficiently compute the optimal solution .
The L0 regularizer measures the parameter sparsity directly and is invariant to the scaling of parameter values , but it can not provide useful gradients , and therefore requires complex optimization techniques . The L1 regularizer is almost everywhere differentiable and can be easily optimized with gradient descent . Yet it is not scale-invariant , causing the same shrinking rate to all parameters , which is inefficient in increasing sparsity .
For the ill-posed fluorescent molecular tomography ( FMT ) inverse problem , the L1 regularization can protect the high-frequency information like edges while effectively reduce the image noise . However , the state-of-the-art L1 regularization-based algorithms for FMT reconstruction are expensive in memory , especially for large-scale problems . An efficient L1 regularization-based reconstruction algorithm based on nonlinear conjugate gradient with restarted strategy is proposed to increase the computational speed with low memory consumption .
To address this issue , in this work we have presented a new approach for software defect prediction by combining genetic algorithm optimization process for feature subspace reduction and deep belief network for pattern learning . Deep belief networks are further improved by applying L1-regularization scheme resulting in better learning process by reducing the overfitting error . This combined model is implemented on SPIE lab software defect database .
Driver gene selection is crucial to understand the heterogeneous system of cancer . To identity cancer driver genes , various statistical strategies have been proposed , especially the L1-type regularization methods have drawn a large amount of attention . However , the statistical approaches have been developed purely from algorithmic and statistical point , and the existing studies have applied the statistical approaches to genomic data analysis without consideration of biological knowledge .
In GSR-NCR , the local sparsity and nonlocal self-similarity of images is simultaneously considered in a unified framework . Different from the previous methods based on sparsity-promoting convex regularization , we extend the non-convex weighted Lp ( 0 < p < 1 ) penalty function on group sparse coefficients of the data matrix , rather than conventional L1-based regularization . To reduce the computational complexity , instead of learning the dictionary with a high computational complexity from natural images , we learn the principle component analysis ( PCA ) based dictionary for each group .
In this paper , we will propose two types of tolerant fuzzy c-means clustering with regularization terms . One is L2-regularization term and the other is L1-regularization one for tolerance vector . Introducing a concept of clusterwise tolerance , we have proposed tolerant fuzzy c-means clustering from the viewpoint of handling data more flexibly .
This algorithm minimizes an objective function of the form φ(Bu ) + 1/2||FpSu - f||2 , where φ is the regularization term which may be nonsmooth . In image reconstruction , the φ term corresponds to total variation smoothing and/or L1 regularization term . The least square term 1/2||FpSu - f||2 is the fidelity term .
We initialize weights using the initialization described in and accordingly ( row -) normalize input feature vectors . On the random graph datasets , we use a hidden layer size of 32 units and omit regularization ( i.e. neither dropout nor L2 regularization ) . subsection : Baselines
In this case , the feature of text is a 1 , 720 dimensional vector . Dropout [ reference ] ) with the keep rate 0.75 and L2 regularization are performed to avoid overfitting . For the generator , we adopt LSTM [ reference ] as the architectures of MANAGER and WORKER to capture the sequence context information .
subsubsection : Training We use categorical cross - entropy along with L2 - regularization as the measure of loss ( ) during training : where is the number of samples / dialogues , is the number of utterances in sample , is the probability distribution of emotion labels for utterance of dialogue , is the expected class label of utterance of dialogue , is the L2 - regularizer weight , and is the set of trainable parameters where We used stochastic gradient descent based Adam optimizer to train our network . Hyperparameters are optimized using grid search ( values are added to the supplementary material ) .
We used mini - batch stochastic gradient decent and empirically found it effective to use a gradient clipping method with growing clipping values for the different tasks ; concretely , we employed the simple function : , where is the number of bi - LSTM layers involved in each task , and is the maximum value . We applied our successive regularization to our model , along with L2 - norm regularization and dropout dropout2014ver . More details are summarized in the supplemental material .
section : D. Performance Comparison The LR and FM models are trained with L2 norm regularization , while FNN , CCPM and PNNs are trained with dropout . By default , we set dropout rate at 0.5 on network hidden layers , which is proved effective in Figure 2 .
subsection : Regularization We use L2 norm regularization on the convolutional kernel parameters with a weight of . We also use the spatial dropout with a rate of after the initial encoder convolution .
subsection : Regularization For regularization , we employ two commonly used techniques : dropout and L2 weight regularization . We apply dropout to prevent co - adaptation .
textabstractWe consider a data assimilation problem for imperfect models . We propose a novel shadowing-based data assimilation method that takes model error into account following the Levenberg-Marquardt regularization approach . We illuminate how the proposed shadowing-based method is related to the weak constraint 4DVar method both analytically and numerically .
The inversion scheme takes the form of an integral equation , which is discretized by means of the method of moments . The measured data are then inverted by means of the conjugate gradient ( CG ) fast Fourier transform algorithm , which incorporates Levenberg-Marquardt regularization and adaptive preconditioning schemes . The reconstruction of the flaw based on simulated as well as measured data , along with some of the salient features of the newly developed CG algorithm are presented . >
To do this , we propose a method for jointly learning the structure and parameters of conditional random fields , formulating these tasks as a convex optimization problem . We consider block-L1 regularization for each set of features associated with an edge , and formalize an efficient projection method to find the globally optimal penalized maximum likelihood solution . We perform extensive numerical experiments comparing the presented method with related methods that approach the structure learning problem differently .
Topology elements among the modeling cues are recovered by the Binary Space Partitioning ( BSP ) technique . The regularity of the building rooftop model is achieved by an implicit regularization process in the framework of Minimum Description Length ( MDL ) combined with Hypothesize and Test ( HAT ) . The parameters governing the MDL optimization are automatically estimated based on Min-Max optimization and Entropy-based weighting method .
The diffractive filter converts spectral information to a spatial code on the sensor pixels . Following a calibration step , this code can be inverted via regularization-based linear algebra to compute the multispectral image . We experimentally demonstrated spectral resolution of 9.6 nm within the visible band ( 430–718 nm ) .
To address this problem , we propose a novel nonconvex structure matrix decomposition model , where using a nonconvex surrogate ( i.e. , the l1 norm of logistic function ) on the singular values of a matrix to approximate the rank function . In addition , our model contains two structural regularizations : a group sparsity induced norm regularization to explore the relationship between each superpixel , making salient object highlighted consistently , and a Laplacian regularization to increase the distance between salient regions and non-salient regions in feature space . Finally , high-level priors are integrated to our model .
However , this method is empirical and implements a global regularization parameter over all uterine sites , which is sub-optimal for EMMI given the severe eccentricity of body-uterus geometry . To address this limitation , we developed a spatial-dependent ( SP ) regularization method that considers both body-uterus eccentricity and EMG noise . We used electrical signals simulated with spherical and realistic geometry models to compare the reconstruction accuracy of the SP method to those of the CRESO and the L-Curve methods .
The aim of this paper is to propose new regularization and filtering techniques for dense and sparse vector fields , and to focus on their application to non-rigid registration . Indeed , most of the regularization energies used in non-rigid registration operate independently on each coordinate of the transformation .
However , SMR does not consider the local geometry of image samples , and it assumes that the training samples should exactly fit a linear model or a strict binary label matrix by left and right regression matrices . In order to enlarge margins between different classes and preserve the intrinsic geometry structure of samples in the transformed space , we will propose dynamic graph regularization and label relaxation-based SMR ( abbreviated as DGRLR-SMR ) method for two-dimensional supervised feature selection . First , the label relaxation SMR is established by relaxing the strict binary label matrix into a slack variable matrix via a nonnegative label relaxation matrix by the $ \varepsilon $ -dragging technique .
In this paper , we investigate the origin of this ill-conditioning and the way in which it influences the resulting filters . Two data-driven subspace regularization approaches are proposed , and those are shown to outperform a regularization approach used in recent literature . The comparison of the methods is based on ground truth data that are recorded in-vivo .
A number of techniques have been proposed in literature to address this problem . In this paper we propose a simple technique called fraternal dropout that takes advantage of dropout to achieve this goal . Specifically , we propose to train two identical copies of an RNN ( that share parameters ) with different dropout masks while minimizing the difference between their ( pre-softmax ) predictions .
Their method uses the same dropout mask at each timestep . fraternal proposed fraternal dropout , which minimizes the differences between outputs from different dropout masks to be invariant to the dropout mask . DBLP :
Neural-network Modelling of Bayesian Learning and Inference L2 Regularization versus Batch and Weight Normalization Progressive optimization of a fuzzy inference system Evolving Stochastic Learning Algorithm based on Tsallis entropic index Dropout Versus Weight Decay for Deep Networks Fundamental differences between Dropout and Weight Decay in Deep Networks Evolutionary Based Weight Decaying Method for Neural Network Training Image categorization for marketing purposes Bridge deck delamination segmentation based on aerial thermography through regularized grayscale morphological reconstruction and gradient statistics Residual Continual Learning An Exponential Learning Rate Schedule for Deep Learning Recent Advances in the MOBJ Algorithm for Training Artifical Neural Networks Distributed Weighted Clustering of Evolving Sensor Data Streams with Noise GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium Incremental Learning in Person Re-Identification In-place Activated BatchNorm for Memory-Optimized Training of DNNs Learning Deep Parsimonious Representations Smooth group L1/2 regularization for input layer of feedforward neural networks Regularization and feature selection in least-squares temporal difference learning DeepHoyer: Learning Sparser Neural Network with Differentiable Scale-Invariant Sparsity Measures Efficient L1 regularization-based reconstruction for fluorescent molecular tomography using restarted nonlinear conjugate gradient. SOFTWARE DEFECT PREDICTION USING DEEP BELIEF NETWORK WITH L1-REGULARIZATION BASED OPTIMIZATION Interaction-Based Feature Selection for Uncovering Cancer Driver Genes Through Copy Number-Driven Expression Level Group-based sparse representation for image compressive sensing reconstruction with non-convex regularization Comparison of tolerant fuzzy c-means clustering with L2- and L1-regularization Partially parallel MR image reconstruction using sensitivity encoding Semi-Supervised Classification with Graph Convolutional Networks Long Text Generation via Adversarial Training with Leaked Information DialogueRNN: An Attentive RNN for Emotion Detection in Conversations A Joint Many-Task Model: Growing a Neural Network for Multiple NLP Tasks Product-Based Neural Networks for User Response Prediction 3D MRI brain tumor segmentation using autoencoder regularization A C-LSTM Neural Network for Text Classification Regularized shadowing-based data assimilation method for imperfect models and its comparison to the weak constraint 4DVar method On a linearized inverse scattering model for a three-dimensional flaw embedded in anisotropic advanced composite materials Structure learning in random fields for heart motion abnormality detection Implicit Regularization for Reconstructing 3D Building Rooftop Models Using Airborne LiDAR Data Computational multispectral video imaging Salient Object Detection Via Nonconvex Structured Matrix Decomposition Spatial-dependent regularization to solve the inverse problem in electromyometrial imaging Isotropic Energies, Filters and Splines for Vector Field Regularization Dynamic Graph Regularization and Label Relaxation-Based Sparse Matrix Regression for Two-Dimensional Feature Selection A data-driven regularization approach for template matching in spike sorting with high-density neural probes Fraternal Dropout Direct Output Connection for a High-Rank Language Model
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CogSci AAAI ICLR NIPS ArXiv 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition NIPS ICML GrC ICIP ICLR AAAI AAAI EMNLP 2016 IEEE 16th International Conference on Data Mining (ICDM) BrainLes@MICCAI ArXiv CVPR CIS EMBC EMNLP
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