A bi-linearity robust estimation method based on a bi-linearity convex optimization theory for an electric power system , comprising : first introducing a bi-linearity theory , and converting a non-linearity measurement equation to linearity measurement equations at two stages ; calculating sparse characteristics of measurement gross errors , and converting the robust estimation to strict convex optimization questions at two stages ; and at each stage , first identifying the sparse measurement gross errors on the basis of ADMM , eliminating the gross errors in the measurement , and then solving by adopting WLS , thus reserving the advantages of the WLS . A test result of an IEEE standard system and a domestic real power grid shows that due to the introduction of the bi-linearity theory , the calculation efficiency of the proposed method is higher than that of the traditional WLS estimator ; and the ADMM technology can well identify the sparse measurement gross errors , so that the estimation precision of the proposed method is better than that of the traditional robust estimator . This formulation yields a continuous optimization problem , rather than a combinatorial one . In the supervised case , this problem is convex , and we tackle it with an instance of the alternating direction method of multipliers ( ADMM ) . In the unsupervised and semi-supervised cases , the optimization problem is nonconvex , and we address it using an expectation-maximization ( EM ) algorithm , where the M-step is implemented via ADMM . In this paper , the sparse and nonconvex noncontinuous l0 norm regularized model is proposed to recover the Poisson noise and blurred image . Then the resulted optimization problem is solved by the alternating direction method of multipliers(ADMM ) scheme and two different approaches are adopted to solve the ADMM scheme in the numerical experiments . Extensive simulation results verify the convergence of the proposed algorithm and indicate that the proposed l0 norm based nonconvex model is efficient and comparable with some state-of-the-art approaches . We show that , thanks to tailored interactions ( i.e. , interactions designed according to a nonconvex alternating direction method of multipliers , or ADMM , scheme ) , the proposed solution is equivalent to solving the centralized control problem . With some communication exchange , required by the ADMM scheme at given synchronization steps , the safety of the robots is preserved , that is , collisions with neighboring robots are avoided and the robots stay within the bounds of the environment . In this work , we tested the proposed method to coordinate three autonomous vessels at a canal intersection . All the steps can be unified into a objective function . We will show that the proposed objective function can be split into several subproblems to solve iteratively using ADMM technique . The experimental results show that the proposed method outperforms the conventional CSMRI method . We define a new VI-criterion to measure the convergence of stochastic algorithms . While the rate of convergence for any iterative algorithms to solve nonsmooth convex optimization problems can not be better than O(1/√t ) , the proposed stochastic ADMM ( SADMM ) is proved to have an O(1/t ) VI-convergence rate for the l1-regularized hinge loss problems without strong convexity and smoothness . The derived VI-convergence results also support the viewpoint that the standard online analysis is too loose to analyze the stochastic setting properly . This paper addresses the optimal scaling of the ADMM method for distributed quadratic programming . Scaled ADMM iterations are first derived for generic equality-constrained quadratic problems and then applied to a class of distributed quadratic problems . In this setting , the scaling corresponds to the step-size and the edge-weights of the underlying communication graph . However , it suffers from several limitations , e.g. , a relative low convergence speed , and an expensive time cost . To this end , in this paper , a novel method , namely the group-based ADMM ( GADMM ) , is proposed for distributed linear classification . In particular , to accelerate the convergence speed and improve global consensus , a group layer is first utilized in GADMM to divide all the slave nodes into several groups . Linear programming ( LP ) decoding using the alternating direction method of multipliers ( ADMM ) has been shown to be an efficient algorithm . A non-convex variation based on the ADMM LP decoder called the ADMM penalized decoder was introduced by Liu et al. ( IEEE ITW , Sep. 2012 ) to close the signal-to-noise ratio ( SNR ) gap between LP decoding and classic belief propagation ( BP ) decoding . This algorithm was shown to achieve or outperform BP decoding at all SNRs , including high SNRs where BP decoding suffers from the error floor effect . In this paper , we similarly generalize the alternating direction method of multipliers ( ADMM ) to Bregman ADMM ( BADMM ) , which allows the choice of different Bregman divergences to exploit the structure of problems . BADMM provides a unified framework for ADMM and its variants , including generalized ADMM , inexact ADMM and Bethe ADMM . We establish the global convergence and the O(1/T ) iteration complexity for BADMM . A rigorous analysis of the novel method establishes linear convergence rate and also guides the choice of parameters to optimize this rate . The novel hybrid update rules of H-CADMM lend themselves to “ in-network acceleration ” that is shown to effect considerable — and essentially “ free-of-charge”—performance boost over the fully decentralized ADMM . Comprehensive numerical tests validate the analysis and showcase the potential of the method in tackling efficiently , widely useful learning tasks . In this paper , ADMM is formulated and applied to a DMPC problem first in the primal domain . The main contribution of this paper is , however , the application of ADMM to the dual of the DMPC problem , introducing an augmented connection graph , which shows considerable improvement in convergence speed and therefore requires a lower number of communications in comparison with primal ADMM . Problems like ( [ reference ] ) containing non - differential terms can not be tackled efficiently with a direct approach , while proximal based methods can be applied . We use the Alternating Direction Method of Multipliers ( ADMM ) that has seen great success recently ( other choices could include f.e . fast iterative soft thresholding ) by first introducing the equivalent splitting version of ( [ reference ] ) This splitting step followed by an augmented Lagrangian method to handle the linear equality constraint is what constitutes ADMM . The success of ADMM for problems is mainly due to the fact that it does not require an exact solution for the iterative sub - optimization problems , but rather an approximate solution . ADMM finds a saddle point with the following iterative scheme Eventually the convergence of the proposed ADMM algorithm ( [ reference ] ) - ( [ reference ] ) can be studied ( and likely proved ) with different mathematical approaches , for example . Solving sub - optimization problems . As an application , our matrix completion model offers a new recommendation algorithm that combines the traditional collaborative filtering and content - based filtering tasks into one unified model . The associated convex non - smooth optimization problem is solved with a well - posed iterative ADMM scheme , which alternates between nuclear proximal operators and approximate solutions of linear systems . Artificial and real data experiments are conducted to study and validate the proposed matrix recovery model , suggesting that in real - life applications where the number of available matrix entries ( ratings ) is usually low and information about products and people taste is available , our model would outperform the standard matrix completion approaches . Thus , linear convergence results of this generalized PPA can be used to better understand the convergence of some widely used algorithms in the literature . We focus on the particular convex minimization context and specify Rockafellar ’s condition to see how to ensure the linear convergence rate for some efficient numerical schemes , including the classical augmented Lagrangian method proposed by Hensen and Powell in 1969 and its relaxed version , the original alternating direction method of multipliers ( ADMM ) by Glowinski and Marrocco in 1975 and its relaxed version ( i.e. , the generalized ADMM by Eckstein and Bertsekas in 1992 ) . Some refined conditions weaker than existing ones are proposed in these particular contexts . Using the proposed approach , the authors formulate 1-bit CS SAR imaging reconstruction problem as an unconstrained optimisation problem where the objective function includes an l 2 data-fidelity term and a non-smooth regularisation function . In order to solve this unconstrained optimisation problem , they use variable splitting and the alternating direction method of multipliers based approach which is computationally efficient and easy to implement . The results from experiments with synthetic and real SAR images validate the effectiveness of the proposed method named as BCST-SAR ( binary CS with time-varying thresholds in SAR imaging ) . By utilizing the transform domains , a joint estimation approach is devised to simultaneously perform WBI suppression and SOI recovery within an optimization framework . Based on the separability property in the optimization , an alternating direction method of multipliers-based approach is developed to efficiently obtain a solution . Finally , simulation results are presented to demonstrate the superior performance of the joint estimation algorithm . The unique solution of the convex optimization problem in Eq . [ reference ] is found by employing an Alternating Direction Method of Multipliers - based algorithm . The final texture model is created by applying PCA on the set of reconstructed feature - based textures acquired from the previous procedure . Given these principles , two principal heuristics are used : reinforcing of good solutions and good steps ( increasing their likelihood ) and rendering successive steps orthogonal . The resulting search algorithm is the covariance matrix adaptation evolution strategy , CMA-ES , that coincides to a great extent to a natural gradient descent . The invariance properties of the CMA-ES are formalized , as are its maximum likelihood and stationarity properties . We present a novel variation of the well-known infomax algorithm of blind source separation . Under natural gradient descent , the infomax algorithm converges to a stationary point of a limiting ordinary differential equation . However , due to the presence of saddle points or local minima of the corresponding likelihood function , the algorithm may be trapped around these “ bad ” stationary points for a long time , especially if the initial data are near them . The function is acquired by modifying a network 's parameters so that a cost function takes the minimum at any time . the cost function is the one introduced by Matsuoka et al. The learning rule is derived from the natural gradient minimization of the cost function . The validity of the proposed method is confirmed by computer simulation . When the input dimension n is much larger than the number of hidden neurons , the complexity of this algorithm is of order O ( n ) . It is confirmed by simulations that the natural gradient descent learning rule is not only efficient but also robust . It is shown how the present algorithms are related to Oja 's principal subspace algorithm , Xu 's algorithm and the Brockett flow . It is also shown that the algorithms are based on the natural gradient ascend/descent methods ( a potential flow in a Riemannian space ) . These policy gradient based algorithms are akin to Stackelberg leadership model and can be extended to model-free settings . We show that if the leader performs natural gradient descent/ascent , then the proposed algorithm has a global sublinear convergence to the Nash equilibrium . Moreover , if the leader adopts a quasi-Newton policy , the algorithm enjoys a global quadratic convergence . A main advantage of these estimators is the flexibility offered by the choice of kernel , which can be used to trade-off statistical efficiency and robustness . On the algorithmic side , we study the geometry induced by MMD on the parameter space and use this to introduce a novel natural gradient descent-like algorithm for efficient implementation of these estimators . We illustrate the relevance of our theoretical results on several classes of models including a discrete-time latent Markov process and two multivariate stochastic differential equation models . Information theoretic criterion is exploited to deduce an objective function for the separation of periodic signals . Minimizing the objective function with natural gradient descent rule , a novel learning algorithm is proposed correspondingly . Computer simulations on signals with temporal structure illustrate the efficiency of the proposed techniques . This paper deals with estimating model parameters in graphical models . We reformulate it as an information geometric optimization problem and introduce a natural gradient descent strategy that incorporates additional meta parameters . We show that our approach is a strong alternative to the celebrated EM approach for learning in graphical models . We use multiple GPUs for data parallelization , and Message Passing Interface ( MPI ) for communication between nodes , which allows us to perform model averaging frequently without losing much time on communication . We investigate the effectiveness of Natural Gradient Stochastic Gradient Descent ( NG-SGD ) and Restricted Boltzmann Machine ( RBM ) pretraining for parallel training in model-averaging framework , and explore the best setups in term of different learning rate schedules , averaging frequencies and minibatch sizes . It is shown that NG-SGD and RBM pretraining benefits parameter-averaging based model training . The architecture , close to that of , is summarized in Figure [ reference ] and Table [ reference ] . The Raspberry Pi 3 model uses 7 layers , and is trained with the lattice - free Maximum Mutual Information ( MMI ) criterion , using natural gradient descent , with a learning rate of 0.0005 and the backstitching trick . We follow the approach described in to create fast acoustic models , namely an HMM topology with one state for each of the 1 , 700 context - dependent senones , operating at a third of the original frame rate . The natural gradient corrects the gradient direction with the inverse Fisher information matrix and , thereby , enables Fisher optimal learning , which ensures the steepest descent in the Riemannian parameter manifold and Fisher efficiency for online learning . The recently introduced Hessian - Free Optimization technique and the Krylov Subspace Descent methods use an extended Gauss - Newton approximation of the Hessian , therefore they can be interpreted as versions of natural gradient descent . Since for neural networks the Fisher information matrix is typically too expensive to compute , different approximations of the natural gradient have been proposed . This paper summarizes information about a method , called sample-path optimization , for optimizing performance functions in certain stochastic systems that can be modeled by simulation . We explain the method , give conditions under which it converges , and display some sample calculations that indicate how it performs . Complexity and computational complexity present in these algorithms make the retrieval task more inefficient . In order to overcome these drawbacks , we proposed a novel fuzzy based optimization technique in the Grid computing environment based on an encrypted text along with Fuzzy rules . We obtained a satisfactory result in keyword search using this novel method . The uncertainty issues prevailing in the WSN makes way for the selection of the cluster head through the optimization algorithms . In this paper , the Fuzzy based optimization approach has been introduced for the optimal selection of the cluster head . This paper proposes the Penguin Fuzzy based Ant colony optimization ( PFuzzyACO ) algorithm for the cluster head selection in the WSN . The problems of VVER in-core fuel management and the ongoing reassessment of VVER refueling design limitations require an application of advanced Western core design technology and methodology to the VVERs , including loading pattern optimization techniques . The implementation of many advanced pressurized water reactor ( PWR ) core and fuel design features in VVER reactors enhances safety and improves fuel efficiency . Display Omitted An integrated particle swarm optimization algorithm for weight minimization of truss structures with sizing and layout variables is developed;.Optimization problems with frequency constraints and static constraints are solved;.The new algorithm is competitive with other state-of-the-art metaheuristic algorithms . Natural frequencies offer useful knowledge on the dynamic response of the structures . In this chapter , we look at the various profiling and optimization tools that are available in the Unreal editor and when testing on the Android target platform . It is usually a good idea to start profiling early and have an eye on the frames per second ( fps ) at any stage of development to eliminate roadblocks when they occur . This study presents tribal particle swarm optimization ( TPSO ) to optimize the parameters of the specific neurofuzzy inference system ( NIS ) for forecasting sunspot numbers . The proposed TPSO uses particle swarm optimization ( PSO ) as evolution strategies of the tribes optimization algorithm ( TOA ) to balance local and global exploration of the search space . Experimental results demonstrated that the proposed TPSO method converges quickly and yields a lower RMS error than other current methods . This methodology works for bacterial colonies and social insects as well as for human social structures . With the CI theory some patterns of human behavior receive formal justification , others can be explained as IQS optimization . The CI formalization assumes that it is a property of a social structure , initializing when individuals interact , and as a result , acquiring the ability to solve new or more complex problems . Confronted with the problem , this paper proposed a user demand description method which is helpful to formalize user demand expression and bridge the gap between user demand and web data sources . Based on user demand description , this paper also proposed user demand set optimization method to eliminate the subset and intersection relationship among user demand set . The experimental results demonstrate that user demand description and its optimization method can well express complex user demand and reduce redundant query cost . In this work , the computational complexity of a hierarchic optimization problem involving in several players is studied . Each player is assigned with a linear objective function . Resent investigations have shown the very good results of digital system ; and circuits optimization using integration of dynamic power management in the design flow . This approach proceed from detection periods of time during which parts of the circuit are not doing useful work and shut them down by either turning off the power supply or the clock signal . We test this model on three tasks : non - uniform motion blur removal , lossy - compression artifact reduction and single image super resolution . We demonstrate that our model substantially outperforms state - of - the - art methods on all these tasks and is significantly faster than optimization - based approaches to deconvolution . Unlike models that directly predict output pixel values , the predicted filter flow is controllable and interpretable , which we demonstrate by visualizing the space of predicted filters for different tasks . section : Related Work Our work is inspired by filter flow , which is an optimization based method for finding a linear transformation relating nearby pixel values in a pair of images . By imposing additional constraints on certain structural properties of these filters , it serves as a general framework for understanding a wide variety of low - level vision problems . While these approaches have been demonstrated on simple few - shot image classification datasets [ reference ] , they have yet to scale to the more complex problems , such as the experiments in this paper . A number of works have approached the problem of few - shot learning from a meta - learning perspective [ reference ][ reference ] , including black - box [ reference ][ reference ][ reference ] and optimization - based approaches [ reference ][ reference ] . While these approaches scale to large - scale image datasets [ reference ] and visual reinforcement learning problems [ reference ] , they typically lack the ability to reason about uncertainty . Our work is most related to methods that combine deep networks and probabilistic methods for few - shot learning [ reference ] . LLE selects a fixed number of neighbors around each data point , and learns a weight coefficient for each neighbor to reconstruct each point as a weighted sum of its neighbors . A second optimization step extracts the point 's feature embedding . Memory networks also share some connections with our work , in particular , if we interpret the neighborhood of a node as the memory , which is used to compute the node features by attending over its values , and then is updated by storing the new features in the same position . subsection : Parameter Settings We use cross - entropy loss as the training objective with Adam - based optimization with 32 batch size . The starting learning rate is 0.0002 with half decay every two epochs . We found this learning rate schedule essential for training the self - attention model . We only update optimization moving - average accumulators for parameters which receive gradient updates at a given step . In all of our experiments we used initial learning rate 0.04 , , , and dropout rates of 0.1 everywhere . We provide class information to G with class - conditional BatchNorm dumoulin2017artistic , devries2017modulating and to D with projection miyato2018cgans . The optimization settings follow zhang2018sagan ( notably employing Spectral Norm in G ) with the modification that we halve the learning rates and take two D steps per G step . For evaluation , we employ moving averages of G ’s weights following karras2018progan , mescheder2018r1gp , yazici2018ema , with a decay of . 3 , in which the main task on training a tree in a random forest is to decide thresholds in the split - nodes and learn the regressors or classes in the leaf - nodes . Rigid regression or linear regression is often employed in the leaf - nodes for the prediction task , because rigid regression has a closed - form solution , while linear regression is an efficient optimization tool , and the LibLinear package [ reference ] can be used to fine - tune its configurations . Compared to conventional random forests , our JMPF scheme has one more step , as shown in the left of Fig . The natural gradient corrects the gradient direction with the inverse Fisher information matrix and , thereby , enables Fisher optimal learning , which ensures the steepest descent in the Riemannian parameter manifold and Fisher efficiency for online learning . The recently introduced Hessian - Free Optimization technique and the Krylov Subspace Descent methods use an extended Gauss - Newton approximation of the Hessian , therefore they can be interpreted as versions of natural gradient descent . Since for neural networks the Fisher information matrix is typically too expensive to compute , different approximations of the natural gradient have been proposed . A striking example within the computer vision community is the improvement on the ImageNet deng2009imagenet classification task when transitioning from AlexNet alexNet12 to VGG vgg16 to GoogLeNet szegedy2015inception to ResNet he2015deep . Unfortunately , greater depth also makes training more challenging , at least when employing a first - order optimization method with randomly initialized layers . As the network grows deeper and more non - linear , the linear approximation of a gradient step becomes increasingly inappropriate . In this work , we develop a deep conditional generative model for structured output prediction using Gaussian latent variables . The model is trained efficiently in the framework of stochastic gradient variational Bayes , and allows for fast prediction using stochastic feed-forward inference . In addition , we provide novel strategies to build robust structured prediction algorithms , such as input noise-injection and multi-scale prediction objective at training . This paper presents the Deep Convolution Inverse Graphics Network ( DC-IGN ) , a model that aims to learn an interpretable representation of images , disentangled with respect to three-dimensional scene structure and viewing transformations such as depth rotations and lighting variations . The DC-IGN model is composed of multiple layers of convolution and de-convolution operators and is trained using the Stochastic Gradient Variational Bayes ( SGVB ) algorithm [ 10 ] . We propose a training procedure to encourage neurons in the graphics code layer to represent a specific transformation ( e.g. pose or light ) . We investigate the use of alternative divergences to Kullback-Leibler ( KL ) in variational inference(VI ) , based on the Variational Dropout \cite{kingma2015}. Stochastic gradient variational Bayes ( SGVB ) \cite{aevb } is a general framework for estimating the evidence lower bound ( ELBO ) in Variational Bayes . In this work , we extend the SGVB estimator with using Alpha-Divergences , which are alternative to divergences to VI ' KL objective . The choice of the inverted Dirichlet and the generalized inverted Dirichlet distributions is motivated by their flexibility and modeling capabilities when dealing with this kind of data , while deploying the Pitman – Yor process prior is justified by its power-law behavior , which makes it a natural choice in real-life application compared with Dirichlet processes for instance . The inference for the resulting models takes into account the challenging problem of feature weighting/selection and is conducted under a Bayesian setting by means of the recently proposed stochastic variational Bayes technique . The efficacy and merits of the proposed approaches are examined using the synthetic data and a challenging real-life application that concerns video background subtraction . We compute the variational posteriors from a mapping structure among latent representation , topics indicator and image-annotation . The stochastic gradient variational Bayes estimator on variational objective is realized by combining the reparameterization trick and Monte Carlo estimator . Finally , we demonstrate the performance of LGMG on LabelMe in terms of held-out likelihood , automatic image annotation with the state-of-the-art models . Then , we introduce a stochastic hidden variable to predict the standard deviation synchronously . The proposed model is derived from variational inference and trained as a stochastic gradient variational Bayes estimator . Simulations are performed to show the correlation between the true residual error and the estimated standard deviation . In this paper , a novel framework named VAEGAN is proposed to address the above issue . In VAEGAN , we first introduce Adversarial Variational Bayes ( AVB ) to train Variational Autoencoders with arbitrarily expressive inference model . By utilizing Generative Adversarial Networks ( GANs ) for implicit variational inference , the inference model provides better approximation to the posterior and maximum-likelihood assignment . Stochastic Variational Bayes Inference . The simultaneous localization and mapping ( SLAM ) problem involves using the measurements of sensors to construct an environmental map , while simultaneously recovering the vehicle trajectory within this map . The model is used to examine the extent to which legislators ' voting records are aligned with constituent preferences , and the implications of that alignment ( or lack thereof ) on subsequent election outcomes . The analysis is based on a Bayesian formalism , with fast inference via a stochastic variational Bayesian analysis . For example , adversarial autoencoders ( AAE ) aae use a universal approximator posterior as the implicit posterior distribution and use adversarial training to match the aggregated posterior of the latent code to the prior distribution . Adversarial variational Bayes ference , avb uses a more general amortized GAN inference framework within a maximum - likelihood learning setting . Another type of GAN inference technique is used in the ALI ali and BiGAN bigan models , which have been shown to approximate maximum likelihood learning ference .
A bi-linearity robust estimation method based on a bi-linearity convex optimization theory for an electric power system , comprising : first introducing a bi-linearity theory , and converting a non-linearity measurement equation to linearity measurement equations at two stages ; calculating sparse characteristics of measurement gross errors , and converting the robust estimation to strict convex optimization questions at two stages ; and at each stage , first identifying the sparse measurement gross errors on the basis of ADMM , eliminating the gross errors in the measurement , and then solving by adopting WLS , thus reserving the advantages of the WLS . A test result of an IEEE standard system and a domestic real power grid shows that due to the introduction of the bi-linearity theory , the calculation efficiency of the proposed method is higher than that of the traditional WLS estimator ; and the ADMM technology can well identify the sparse measurement gross errors , so that the estimation precision of the proposed method is better than that of the traditional robust estimator .
This formulation yields a continuous optimization problem , rather than a combinatorial one . In the supervised case , this problem is convex , and we tackle it with an instance of the alternating direction method of multipliers ( ADMM ) . In the unsupervised and semi-supervised cases , the optimization problem is nonconvex , and we address it using an expectation-maximization ( EM ) algorithm , where the M-step is implemented via ADMM .
In this paper , the sparse and nonconvex noncontinuous l0 norm regularized model is proposed to recover the Poisson noise and blurred image . Then the resulted optimization problem is solved by the alternating direction method of multipliers(ADMM ) scheme and two different approaches are adopted to solve the ADMM scheme in the numerical experiments . Extensive simulation results verify the convergence of the proposed algorithm and indicate that the proposed l0 norm based nonconvex model is efficient and comparable with some state-of-the-art approaches .
We show that , thanks to tailored interactions ( i.e. , interactions designed according to a nonconvex alternating direction method of multipliers , or ADMM , scheme ) , the proposed solution is equivalent to solving the centralized control problem . With some communication exchange , required by the ADMM scheme at given synchronization steps , the safety of the robots is preserved , that is , collisions with neighboring robots are avoided and the robots stay within the bounds of the environment . In this work , we tested the proposed method to coordinate three autonomous vessels at a canal intersection .
All the steps can be unified into a objective function . We will show that the proposed objective function can be split into several subproblems to solve iteratively using ADMM technique . The experimental results show that the proposed method outperforms the conventional CSMRI method .
We define a new VI-criterion to measure the convergence of stochastic algorithms . While the rate of convergence for any iterative algorithms to solve nonsmooth convex optimization problems can not be better than O(1/√t ) , the proposed stochastic ADMM ( SADMM ) is proved to have an O(1/t ) VI-convergence rate for the l1-regularized hinge loss problems without strong convexity and smoothness . The derived VI-convergence results also support the viewpoint that the standard online analysis is too loose to analyze the stochastic setting properly .
This paper addresses the optimal scaling of the ADMM method for distributed quadratic programming . Scaled ADMM iterations are first derived for generic equality-constrained quadratic problems and then applied to a class of distributed quadratic problems . In this setting , the scaling corresponds to the step-size and the edge-weights of the underlying communication graph .
However , it suffers from several limitations , e.g. , a relative low convergence speed , and an expensive time cost . To this end , in this paper , a novel method , namely the group-based ADMM ( GADMM ) , is proposed for distributed linear classification . In particular , to accelerate the convergence speed and improve global consensus , a group layer is first utilized in GADMM to divide all the slave nodes into several groups .
Linear programming ( LP ) decoding using the alternating direction method of multipliers ( ADMM ) has been shown to be an efficient algorithm . A non-convex variation based on the ADMM LP decoder called the ADMM penalized decoder was introduced by Liu et al. ( IEEE ITW , Sep. 2012 ) to close the signal-to-noise ratio ( SNR ) gap between LP decoding and classic belief propagation ( BP ) decoding . This algorithm was shown to achieve or outperform BP decoding at all SNRs , including high SNRs where BP decoding suffers from the error floor effect .
In this paper , we similarly generalize the alternating direction method of multipliers ( ADMM ) to Bregman ADMM ( BADMM ) , which allows the choice of different Bregman divergences to exploit the structure of problems . BADMM provides a unified framework for ADMM and its variants , including generalized ADMM , inexact ADMM and Bethe ADMM . We establish the global convergence and the O(1/T ) iteration complexity for BADMM .
A rigorous analysis of the novel method establishes linear convergence rate and also guides the choice of parameters to optimize this rate . The novel hybrid update rules of H-CADMM lend themselves to “ in-network acceleration ” that is shown to effect considerable — and essentially “ free-of-charge”—performance boost over the fully decentralized ADMM . Comprehensive numerical tests validate the analysis and showcase the potential of the method in tackling efficiently , widely useful learning tasks .
In this paper , ADMM is formulated and applied to a DMPC problem first in the primal domain . The main contribution of this paper is , however , the application of ADMM to the dual of the DMPC problem , introducing an augmented connection graph , which shows considerable improvement in convergence speed and therefore requires a lower number of communications in comparison with primal ADMM .
Problems like ( [ reference ] ) containing non - differential terms can not be tackled efficiently with a direct approach , while proximal based methods can be applied . We use the Alternating Direction Method of Multipliers ( ADMM ) that has seen great success recently ( other choices could include f.e . fast iterative soft thresholding ) by first introducing the equivalent splitting version of ( [ reference ] ) This splitting step followed by an augmented Lagrangian method to handle the linear equality constraint is what constitutes ADMM . The success of ADMM for problems is mainly due to the fact that it does not require an exact solution for the iterative sub - optimization problems , but rather an approximate solution .
ADMM finds a saddle point with the following iterative scheme Eventually the convergence of the proposed ADMM algorithm ( [ reference ] ) - ( [ reference ] ) can be studied ( and likely proved ) with different mathematical approaches , for example . Solving sub - optimization problems .
As an application , our matrix completion model offers a new recommendation algorithm that combines the traditional collaborative filtering and content - based filtering tasks into one unified model . The associated convex non - smooth optimization problem is solved with a well - posed iterative ADMM scheme , which alternates between nuclear proximal operators and approximate solutions of linear systems . Artificial and real data experiments are conducted to study and validate the proposed matrix recovery model , suggesting that in real - life applications where the number of available matrix entries ( ratings ) is usually low and information about products and people taste is available , our model would outperform the standard matrix completion approaches .
Thus , linear convergence results of this generalized PPA can be used to better understand the convergence of some widely used algorithms in the literature . We focus on the particular convex minimization context and specify Rockafellar ’s condition to see how to ensure the linear convergence rate for some efficient numerical schemes , including the classical augmented Lagrangian method proposed by Hensen and Powell in 1969 and its relaxed version , the original alternating direction method of multipliers ( ADMM ) by Glowinski and Marrocco in 1975 and its relaxed version ( i.e. , the generalized ADMM by Eckstein and Bertsekas in 1992 ) . Some refined conditions weaker than existing ones are proposed in these particular contexts .
Using the proposed approach , the authors formulate 1-bit CS SAR imaging reconstruction problem as an unconstrained optimisation problem where the objective function includes an l 2 data-fidelity term and a non-smooth regularisation function . In order to solve this unconstrained optimisation problem , they use variable splitting and the alternating direction method of multipliers based approach which is computationally efficient and easy to implement . The results from experiments with synthetic and real SAR images validate the effectiveness of the proposed method named as BCST-SAR ( binary CS with time-varying thresholds in SAR imaging ) .
By utilizing the transform domains , a joint estimation approach is devised to simultaneously perform WBI suppression and SOI recovery within an optimization framework . Based on the separability property in the optimization , an alternating direction method of multipliers-based approach is developed to efficiently obtain a solution . Finally , simulation results are presented to demonstrate the superior performance of the joint estimation algorithm .
The unique solution of the convex optimization problem in Eq . [ reference ] is found by employing an Alternating Direction Method of Multipliers - based algorithm . The final texture model is created by applying PCA on the set of reconstructed feature - based textures acquired from the previous procedure .
Given these principles , two principal heuristics are used : reinforcing of good solutions and good steps ( increasing their likelihood ) and rendering successive steps orthogonal . The resulting search algorithm is the covariance matrix adaptation evolution strategy , CMA-ES , that coincides to a great extent to a natural gradient descent . The invariance properties of the CMA-ES are formalized , as are its maximum likelihood and stationarity properties .
We present a novel variation of the well-known infomax algorithm of blind source separation . Under natural gradient descent , the infomax algorithm converges to a stationary point of a limiting ordinary differential equation . However , due to the presence of saddle points or local minima of the corresponding likelihood function , the algorithm may be trapped around these “ bad ” stationary points for a long time , especially if the initial data are near them .
The function is acquired by modifying a network 's parameters so that a cost function takes the minimum at any time . the cost function is the one introduced by Matsuoka et al. The learning rule is derived from the natural gradient minimization of the cost function . The validity of the proposed method is confirmed by computer simulation .
When the input dimension n is much larger than the number of hidden neurons , the complexity of this algorithm is of order O ( n ) . It is confirmed by simulations that the natural gradient descent learning rule is not only efficient but also robust .
It is shown how the present algorithms are related to Oja 's principal subspace algorithm , Xu 's algorithm and the Brockett flow . It is also shown that the algorithms are based on the natural gradient ascend/descent methods ( a potential flow in a Riemannian space ) .
These policy gradient based algorithms are akin to Stackelberg leadership model and can be extended to model-free settings . We show that if the leader performs natural gradient descent/ascent , then the proposed algorithm has a global sublinear convergence to the Nash equilibrium . Moreover , if the leader adopts a quasi-Newton policy , the algorithm enjoys a global quadratic convergence .
A main advantage of these estimators is the flexibility offered by the choice of kernel , which can be used to trade-off statistical efficiency and robustness . On the algorithmic side , we study the geometry induced by MMD on the parameter space and use this to introduce a novel natural gradient descent-like algorithm for efficient implementation of these estimators . We illustrate the relevance of our theoretical results on several classes of models including a discrete-time latent Markov process and two multivariate stochastic differential equation models .
Information theoretic criterion is exploited to deduce an objective function for the separation of periodic signals . Minimizing the objective function with natural gradient descent rule , a novel learning algorithm is proposed correspondingly . Computer simulations on signals with temporal structure illustrate the efficiency of the proposed techniques .
This paper deals with estimating model parameters in graphical models . We reformulate it as an information geometric optimization problem and introduce a natural gradient descent strategy that incorporates additional meta parameters . We show that our approach is a strong alternative to the celebrated EM approach for learning in graphical models .
We use multiple GPUs for data parallelization , and Message Passing Interface ( MPI ) for communication between nodes , which allows us to perform model averaging frequently without losing much time on communication . We investigate the effectiveness of Natural Gradient Stochastic Gradient Descent ( NG-SGD ) and Restricted Boltzmann Machine ( RBM ) pretraining for parallel training in model-averaging framework , and explore the best setups in term of different learning rate schedules , averaging frequencies and minibatch sizes . It is shown that NG-SGD and RBM pretraining benefits parameter-averaging based model training .
The architecture , close to that of , is summarized in Figure [ reference ] and Table [ reference ] . The Raspberry Pi 3 model uses 7 layers , and is trained with the lattice - free Maximum Mutual Information ( MMI ) criterion , using natural gradient descent , with a learning rate of 0.0005 and the backstitching trick . We follow the approach described in to create fast acoustic models , namely an HMM topology with one state for each of the 1 , 700 context - dependent senones , operating at a third of the original frame rate .
The natural gradient corrects the gradient direction with the inverse Fisher information matrix and , thereby , enables Fisher optimal learning , which ensures the steepest descent in the Riemannian parameter manifold and Fisher efficiency for online learning . The recently introduced Hessian - Free Optimization technique and the Krylov Subspace Descent methods use an extended Gauss - Newton approximation of the Hessian , therefore they can be interpreted as versions of natural gradient descent . Since for neural networks the Fisher information matrix is typically too expensive to compute , different approximations of the natural gradient have been proposed .
This paper summarizes information about a method , called sample-path optimization , for optimizing performance functions in certain stochastic systems that can be modeled by simulation . We explain the method , give conditions under which it converges , and display some sample calculations that indicate how it performs .
Complexity and computational complexity present in these algorithms make the retrieval task more inefficient . In order to overcome these drawbacks , we proposed a novel fuzzy based optimization technique in the Grid computing environment based on an encrypted text along with Fuzzy rules . We obtained a satisfactory result in keyword search using this novel method .
The uncertainty issues prevailing in the WSN makes way for the selection of the cluster head through the optimization algorithms . In this paper , the Fuzzy based optimization approach has been introduced for the optimal selection of the cluster head . This paper proposes the Penguin Fuzzy based Ant colony optimization ( PFuzzyACO ) algorithm for the cluster head selection in the WSN .
The problems of VVER in-core fuel management and the ongoing reassessment of VVER refueling design limitations require an application of advanced Western core design technology and methodology to the VVERs , including loading pattern optimization techniques . The implementation of many advanced pressurized water reactor ( PWR ) core and fuel design features in VVER reactors enhances safety and improves fuel efficiency .
Display Omitted An integrated particle swarm optimization algorithm for weight minimization of truss structures with sizing and layout variables is developed;.Optimization problems with frequency constraints and static constraints are solved;.The new algorithm is competitive with other state-of-the-art metaheuristic algorithms . Natural frequencies offer useful knowledge on the dynamic response of the structures .
In this chapter , we look at the various profiling and optimization tools that are available in the Unreal editor and when testing on the Android target platform . It is usually a good idea to start profiling early and have an eye on the frames per second ( fps ) at any stage of development to eliminate roadblocks when they occur .
This study presents tribal particle swarm optimization ( TPSO ) to optimize the parameters of the specific neurofuzzy inference system ( NIS ) for forecasting sunspot numbers . The proposed TPSO uses particle swarm optimization ( PSO ) as evolution strategies of the tribes optimization algorithm ( TOA ) to balance local and global exploration of the search space . Experimental results demonstrated that the proposed TPSO method converges quickly and yields a lower RMS error than other current methods .
This methodology works for bacterial colonies and social insects as well as for human social structures . With the CI theory some patterns of human behavior receive formal justification , others can be explained as IQS optimization . The CI formalization assumes that it is a property of a social structure , initializing when individuals interact , and as a result , acquiring the ability to solve new or more complex problems .
Confronted with the problem , this paper proposed a user demand description method which is helpful to formalize user demand expression and bridge the gap between user demand and web data sources . Based on user demand description , this paper also proposed user demand set optimization method to eliminate the subset and intersection relationship among user demand set . The experimental results demonstrate that user demand description and its optimization method can well express complex user demand and reduce redundant query cost .
In this work , the computational complexity of a hierarchic optimization problem involving in several players is studied . Each player is assigned with a linear objective function .
Resent investigations have shown the very good results of digital system ; and circuits optimization using integration of dynamic power management in the design flow . This approach proceed from detection periods of time during which parts of the circuit are not doing useful work and shut them down by either turning off the power supply or the clock signal .
We test this model on three tasks : non - uniform motion blur removal , lossy - compression artifact reduction and single image super resolution . We demonstrate that our model substantially outperforms state - of - the - art methods on all these tasks and is significantly faster than optimization - based approaches to deconvolution . Unlike models that directly predict output pixel values , the predicted filter flow is controllable and interpretable , which we demonstrate by visualizing the space of predicted filters for different tasks .
section : Related Work Our work is inspired by filter flow , which is an optimization based method for finding a linear transformation relating nearby pixel values in a pair of images . By imposing additional constraints on certain structural properties of these filters , it serves as a general framework for understanding a wide variety of low - level vision problems .
While these approaches have been demonstrated on simple few - shot image classification datasets [ reference ] , they have yet to scale to the more complex problems , such as the experiments in this paper . A number of works have approached the problem of few - shot learning from a meta - learning perspective [ reference ][ reference ] , including black - box [ reference ][ reference ][ reference ] and optimization - based approaches [ reference ][ reference ] . While these approaches scale to large - scale image datasets [ reference ] and visual reinforcement learning problems [ reference ] , they typically lack the ability to reason about uncertainty . Our work is most related to methods that combine deep networks and probabilistic methods for few - shot learning
[ reference ] . LLE selects a fixed number of neighbors around each data point , and learns a weight coefficient for each neighbor to reconstruct each point as a weighted sum of its neighbors . A second optimization step extracts the point 's feature embedding . Memory networks also share some connections with our work , in particular , if we interpret the neighborhood of a node as the memory , which is used to compute the node features by attending over its values , and then is updated by storing the new features in the same position .
subsection : Parameter Settings We use cross - entropy loss as the training objective with Adam - based optimization with 32 batch size . The starting learning rate is 0.0002 with half decay every two epochs .
We found this learning rate schedule essential for training the self - attention model . We only update optimization moving - average accumulators for parameters which receive gradient updates at a given step . In all of our experiments we used initial learning rate 0.04 , , , and dropout rates of 0.1 everywhere .
We provide class information to G with class - conditional BatchNorm dumoulin2017artistic , devries2017modulating and to D with projection miyato2018cgans . The optimization settings follow zhang2018sagan ( notably employing Spectral Norm in G ) with the modification that we halve the learning rates and take two D steps per G step . For evaluation , we employ moving averages of G ’s weights following karras2018progan , mescheder2018r1gp , yazici2018ema , with a decay of .
3 , in which the main task on training a tree in a random forest is to decide thresholds in the split - nodes and learn the regressors or classes in the leaf - nodes . Rigid regression or linear regression is often employed in the leaf - nodes for the prediction task , because rigid regression has a closed - form solution , while linear regression is an efficient optimization tool , and the LibLinear package [ reference ] can be used to fine - tune its configurations . Compared to conventional random forests , our JMPF scheme has one more step , as shown in the left of Fig .
The natural gradient corrects the gradient direction with the inverse Fisher information matrix and , thereby , enables Fisher optimal learning , which ensures the steepest descent in the Riemannian parameter manifold and Fisher efficiency for online learning . The recently introduced Hessian - Free Optimization technique and the Krylov Subspace Descent methods use an extended Gauss - Newton approximation of the Hessian , therefore they can be interpreted as versions of natural gradient descent . Since for neural networks the Fisher information matrix is typically too expensive to compute , different approximations of the natural gradient have been proposed .
A striking example within the computer vision community is the improvement on the ImageNet deng2009imagenet classification task when transitioning from AlexNet alexNet12 to VGG vgg16 to GoogLeNet szegedy2015inception to ResNet he2015deep . Unfortunately , greater depth also makes training more challenging , at least when employing a first - order optimization method with randomly initialized layers . As the network grows deeper and more non - linear , the linear approximation of a gradient step becomes increasingly inappropriate .
In this work , we develop a deep conditional generative model for structured output prediction using Gaussian latent variables . The model is trained efficiently in the framework of stochastic gradient variational Bayes , and allows for fast prediction using stochastic feed-forward inference . In addition , we provide novel strategies to build robust structured prediction algorithms , such as input noise-injection and multi-scale prediction objective at training .
This paper presents the Deep Convolution Inverse Graphics Network ( DC-IGN ) , a model that aims to learn an interpretable representation of images , disentangled with respect to three-dimensional scene structure and viewing transformations such as depth rotations and lighting variations . The DC-IGN model is composed of multiple layers of convolution and de-convolution operators and is trained using the Stochastic Gradient Variational Bayes ( SGVB ) algorithm [ 10 ] . We propose a training procedure to encourage neurons in the graphics code layer to represent a specific transformation ( e.g. pose or light ) .
We investigate the use of alternative divergences to Kullback-Leibler ( KL ) in variational inference(VI ) , based on the Variational Dropout \cite{kingma2015}. Stochastic gradient variational Bayes ( SGVB ) \cite{aevb } is a general framework for estimating the evidence lower bound ( ELBO ) in Variational Bayes . In this work , we extend the SGVB estimator with using Alpha-Divergences , which are alternative to divergences to VI ' KL objective .
The choice of the inverted Dirichlet and the generalized inverted Dirichlet distributions is motivated by their flexibility and modeling capabilities when dealing with this kind of data , while deploying the Pitman – Yor process prior is justified by its power-law behavior , which makes it a natural choice in real-life application compared with Dirichlet processes for instance . The inference for the resulting models takes into account the challenging problem of feature weighting/selection and is conducted under a Bayesian setting by means of the recently proposed stochastic variational Bayes technique . The efficacy and merits of the proposed approaches are examined using the synthetic data and a challenging real-life application that concerns video background subtraction .
We compute the variational posteriors from a mapping structure among latent representation , topics indicator and image-annotation . The stochastic gradient variational Bayes estimator on variational objective is realized by combining the reparameterization trick and Monte Carlo estimator . Finally , we demonstrate the performance of LGMG on LabelMe in terms of held-out likelihood , automatic image annotation with the state-of-the-art models .
Then , we introduce a stochastic hidden variable to predict the standard deviation synchronously . The proposed model is derived from variational inference and trained as a stochastic gradient variational Bayes estimator . Simulations are performed to show the correlation between the true residual error and the estimated standard deviation .
In this paper , a novel framework named VAEGAN is proposed to address the above issue . In VAEGAN , we first introduce Adversarial Variational Bayes ( AVB ) to train Variational Autoencoders with arbitrarily expressive inference model . By utilizing Generative Adversarial Networks ( GANs ) for implicit variational inference , the inference model provides better approximation to the posterior and maximum-likelihood assignment .
Stochastic Variational Bayes Inference . The simultaneous localization and mapping ( SLAM ) problem involves using the measurements of sensors to construct an environmental map , while simultaneously recovering the vehicle trajectory within this map .
The model is used to examine the extent to which legislators ' voting records are aligned with constituent preferences , and the implications of that alignment ( or lack thereof ) on subsequent election outcomes . The analysis is based on a Bayesian formalism , with fast inference via a stochastic variational Bayesian analysis .
For example , adversarial autoencoders ( AAE ) aae use a universal approximator posterior as the implicit posterior distribution and use adversarial training to match the aggregated posterior of the latent code to the prior distribution . Adversarial variational Bayes ference , avb uses a more general amortized GAN inference framework within a maximum - likelihood learning setting . Another type of GAN inference technique is used in the ALI ali and BiGAN bigan models , which have been shown to approximate maximum likelihood learning ference .
Bi-linearity robust estimation method based on bi-linearity convex optimization theory for electric power system Bayesian image segmentation using hidden fields: Supervised, unsupervised, and semi-supervised formulations Wavelet frame based Poisson noise removal and image deblurring Coordination of Multiple Vessels Via Distributed Nonlinear Model Predictive Control Compressed sensing MRI using total variation regularization with K-space decomposition Stochastic Learning via Optimizing the Variational Inequalities Optimal scaling of the ADMM algorithm for distributed quadratic programming Group-Based Alternating Direction Method of Multipliers for Distributed Linear Classification Instanton search algorithm for the ADMM penalized decoder Bregman Alternating Direction Method of Multipliers Hybrid ADMM: a unifying and fast approach to decentralized optimization ADMM-based distributed model predictive control: Primal and dual approaches Matrix Completion on Graphs On the Optimal Linear Convergence Rate of a Generalized Proximal Point Algorithm One-bit compressive sensing with time-varying thresholds in synthetic aperture radar imaging Joint Wideband Interference Suppression and SAR Signal Recovery Based on Sparse Representations 3D Face Morphable Models "In-the-Wild" Principled Design of Continuous Stochastic Search: From Theory to Practice Convergence analysis of a randomly perturbed infomax algorithm for blind source separation Blind Separation for Convolutive Mixtures of Non-stationary Signals Statistical learning by natural gradient descent A unified algorithm for principal and minor components extraction Global Convergence of Policy Gradient for Sequential Zero-Sum Linear Quadratic Dynamic Games Statistical Inference for Generative Models with Maximum Mean Discrepancy Robust Techniques for Sequential Signal Separation NGO-GM: Natural Gradient Optimization for Graphical Models Experiments on Parallel Training of Deep Neural Network using Model Averaging Snips Voice Platform: an embedded Spoken Language Understanding system for private-by-design voice interfaces Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs) Sample-path optimization in simulation Applying Local Optimization Algorithms in Clustering Combination with Diversity Maximization PFuzzyACO: Fuzzy-based Optimization Approach for Energy-aware Cluster Head Selection in WSN Application of Penn State optimization techniques to VVER-1000 reload design Sizing and layout design of truss structures under dynamic and static constraints with an integrated particle swarm optimization algorithm Performance, Profiling, and Optimizations Neurofuzzy inference systems based on tribal particle swarm optimization for forecasting sunspot numbers A formal definition of the phenomenon of collective intelligence and its IQ measure User Demand Description and Optimization in Web Data Management On Computational Complexity of Hierarchical Optimization Register transfer low power design based on controller decomposition Image Reconstruction with Predictive Filter Flow Probabilistic Model-Agnostic Meta-Learning Graph Attention Networks Shortcut-Stacked Sentence Encoders for Multi-Domain Inference Linguistically-Informed Self-Attention for Semantic Role Labeling Large Scale GAN Training for High Fidelity Natural Image Synthesis Joint maximum purity forest with application to image super-resolution Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs) FractalNet: Ultra-Deep Neural Networks without Residuals Learning Structured Output Representation using Deep Conditional Generative Models Deep Convolutional Inverse Graphics Network Alpha-Divergences in Variational Dropout Nonparametric Hierarchical Bayesian Models for Positive Data Clustering Based on Inverted Dirichlet-Based Distributions Latent Gaussian-Multinomial Generative Model for Annotated Data Uncertainty Estimation in the Neural Model for Aeromagnetic Compensation VAEGAN: A Collaborative Filtering Framework based on Adversarial Variational Autoencoders Robust Linear-Complexity Approach to Full SLAM Problems: Stochastic Variational Bayes Inference Evaluating U.S. Electoral Representation with a Joint Statistical Model of Congressional Roll-Calls, Legislative Text, and Voter Registration Data PixelGAN Autoencoders
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EUSIPCO ECC ICIP CDC ISIT NIPS CDC NIPS 2014 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Theory and Principled Methods for the Design of Metaheuristics ICONIP ArXiv ICLR Winter Simulation Conference ICICS ArXiv NeurIPS ICLR RepEval@EMNLP EMNLP ICLR J. Electronic Imaging ICLR ICLR NIPS NIPS PAKDD (1) IJCAI VTC-Fall KDD NIPS
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