Online Learning for Matrix Factorization and Sparse Coding

Discriminative Sparse Coding on Multi-Manifold for Data Representation and Classification

Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics, etc. However, the conventional sparse coding algorithms and its manifold regularized variants (graph sparse coding and Laplacian sparse coding), learn the codebook and codes in a unsupervised manner and neglect the class information available in the training set. To address this problem, in this paper we propose a novel discriminative sparse coding method based on multi-manifold, by learning discriminative class-conditional codeb…

Decoding the Encoding of Functional Brain Networks: an fMRI Classification Comparison of Non-negative Matrix Factorization (NMF), Independent Component Analysis (ICA), and Sparse Coding Algorithms

Brain networks in fMRI are typically identified using spatial independent component analysis (ICA), yet mathematical constraints such as sparse coding and positivity both provide alternate biologically-plausible frameworks for generating brain networks. Non-negative Matrix Factorization (NMF) would suppress negative BOLD signal by enforcing positivity. Spatial sparse coding algorithms ($L1$ Regularized Learning and K-SVD) would impose local specialization and a discouragement of multitasking, where the total observed activity in a single voxel originates from a restricted number of possible br…

Understanding Trainable Sparse Coding via Matrix Factorization

Sparse coding is a core building block in many data analysis and machine learning pipelines. Typically it is solved by relying on generic optimization techniques, that are optimal in the class of first-order methods for non-smooth, convex functions, such as the Iterative Soft Thresholding Algorithm and its accelerated version (ISTA, FISTA). However, these methods don't exploit the particular structure of the problem at hand nor the input data distribution. An acceleration using neural networks was proposed in \cite{Gregor10}, coined LISTA, which showed empirically that one could achieve high q…

Data embedding and prediction by sparse tropical matrix factorization

Matrix factorization methods are linear models, with limited capability to model complex relations. In our work, we use tropical semiring to introduce non-linearity into matrix factorization models. We propose a method called Sparse Tropical Matrix Factorization (STMF) for the estimation of missing (unknown) values. We evaluate the efficiency of the STMF method on both synthetic data and biological data in the form of gene expression measurements downloaded from The Cancer Genome Atlas (TCGA) database. Tests on unique synthetic data showed that STMF approximation achieves a higher correlation …

Non-Negative Kernel Sparse Coding for the Classification of Motion Data

We are interested in the decomposition of motion data into a sparse linear combination of base functions which enable efficient data processing. We combine two prominent frameworks: dynamic time warping (DTW), which offers particularly successful pairwise motion data comparison, and sparse coding (SC), which enables an automatic decomposition of vectorial data into a sparse linear combination of base vectors. We enhance SC as follows: an efficient kernelization which extends its application domain to general similarity data such as offered by DTW, and its restriction to non-negative linear rep…

Sparse Coding and Dictionary Learning for Symmetric Positive Definite Matrices: A Kernel Approach

Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of symmetric positive definite matrices, which form a Riemannian manifold. With the aid of the recently introduced Stein kernel (related to a symmetric version of Bregman matrix divergence), we propose to perform sparse coding by embedding Riemannian manifolds into reproducing kernel Hilbert spaces. This leads to a convex and kernel version of the Lasso problem, which…

稀疏矩阵分解中的自动超参数调优

Automatic Hyperparameter Tuning in Sparse Matrix Factorization

研究贝叶斯框架下稀疏矩阵分解的超参数调优问题，基于变分贝叶斯方法的解析解提出评估归一化因子零点的新型数值调优方法，并在真实稀疏矩阵重建中表现优异。

矩阵分解在fMRI数据上的性能评估

Performance evaluation of matrix factorization for fMRI data

本研究将多种矩阵分解方法应用于人类全脑fMRI数据，验证全脑信息表征的稀疏编码假设，发现高稀疏度稀疏MF及近似稀疏方法的特征分类视觉刺激更准确。

DICOD: Distributed Convolutional Sparse Coding

In this paper, we introduce DICOD, a convolutional sparse coding algorithm which builds shift invariant representations for long signals. This algorithm is designed to run in a distributed setting, with local message passing, making it communication efficient. It is based on coordinate descent and uses locally greedy updates which accelerate the resolution compared to greedy coordinate selection. We prove the convergence of this algorithm and highlight its computational speed-up which is super-linear in the number of cores used. We also provide empirical evidence for the acceleration propertie…

Spike-and-Slab Sparse Coding for Unsupervised Feature Discovery

We consider the problem of using a factor model we call {\em spike-and-slab sparse coding} (S3C) to learn features for a classification task. The S3C model resembles both the spike-and-slab RBM and sparse coding. Since exact inference in this model is intractable, we derive a structured variational inference procedure and employ a variational EM training algorithm. Prior work on approximate inference for this model has not prioritized the ability to exploit parallel architectures and scale to enormous problem sizes. We present an inference procedure appropriate for use with GPUs which allows u…

Learning Word Representations with Hierarchical Sparse Coding

We propose a new method for learning word representations using hierarchical regularization in sparse coding inspired by the linguistic study of word meanings. We show an efficient learning algorithm based on stochastic proximal methods that is significantly faster than previous approaches, making it possible to perform hierarchical sparse coding on a corpus of billions of word tokens. Experiments on various benchmark tasks---word similarity ranking, analogies, sentence completion, and sentiment analysis---demonstrate that the method outperforms or is competitive with state-of-the-art methods.…

Sparse Coding Frontend for Robust Neural Networks

Deep Neural Networks are known to be vulnerable to small, adversarially crafted, perturbations. The current most effective defense methods against these adversarial attacks are variants of adversarial training. In this paper, we introduce a radically different defense trained only on clean images: a sparse coding based frontend which significantly attenuates adversarial attacks before they reach the classifier. We evaluate our defense on CIFAR-10 dataset under a wide range of attack types (including Linf , L2, and L1 bounded attacks), demonstrating its promise as a general-purpose approach for…

Uncertainty propagation in neural networks for sparse coding

A novel method to propagate uncertainty through the soft-thresholding nonlinearity is proposed in this paper. At every layer the current distribution of the target vector is represented as a spike and slab distribution, which represents the probabilities of each variable being zero, or Gaussian-distributed. Using the proposed method of uncertainty propagation, the gradients of the logarithms of normalisation constants are derived, that can be used to update a weight distribution. A novel Bayesian neural network for sparse coding is designed utilising both the proposed method of uncertainty pro…

Dictionary-based Low-Rank Approximations and the Mixed Sparse Coding problem

Constrained tensor and matrix factorization models allow to extract interpretable patterns from multiway data. Therefore identifiability properties and efficient algorithms for constrained low-rank approximations are nowadays important research topics. This work deals with columns of factor matrices of a low-rank approximation being sparse in a known and possibly overcomplete basis, a model coined as Dictionary-based Low-Rank Approximation (DLRA). While earlier contributions focused on finding factor columns inside a dictionary of candidate columns, i.e. one-sparse approximations, this work is…

Sparse coding for multitask and transfer learning

We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear combinations of the atoms of a dictionary on a high or infinite dimensional space. This assumption, together with the large quantity of available data in the multitask and transfer learning settings, allows a principled choice of the dictionary. We provide bounds on the generalization error of this approach, for both settings. Numerical experiments on one synthetic and…

Word Equations: Inherently Interpretable Sparse Word Embeddingsthrough Sparse Coding

Word embeddings are a powerful natural language processing technique, but they are extremely difficult to interpret. To enable interpretable NLP models, we create vectors where each dimension is inherently interpretable. By inherently interpretable, we mean a system where each dimension is associated with some human understandable hint that can describe the meaning of that dimension. In order to create more interpretable word embeddings, we transform pretrained dense word embeddings into sparse embeddings. These new embeddings are inherently interpretable: each of their dimensions is created f…

Variational Sparse Coding with Learned Thresholding

Sparse coding strategies have been lauded for their parsimonious representations of data that leverage low dimensional structure. However, inference of these codes typically relies on an optimization procedure with poor computational scaling in high-dimensional problems. For example, sparse inference in the representations learned in the high-dimensional intermediary layers of deep neural networks (DNNs) requires an iterative minimization to be performed at each training step. As such, recent, quick methods in variational inference have been proposed to infer sparse codes by learning a distrib…

When coding meets ranking: A joint framework based on local learning

Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points plays an important role. Up to now, these two problems have always been considered separately, assuming that data coding and ranking are two independent and irrelevant problems. However, is there any internal relationship between sparse coding and ranking score learning? If yes, how to explore and make use of this internal relationship? In this paper, we tr…

Multivariate Convolutional Sparse Coding with Low Rank Tensor

This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model achieves a significantly more efficient encoding of the multivariate signal-particularly in the high order/ dimension setting-resulting in better performance. We prove that our model is closely related to the Kruskal tensor regression problem, offering interesting theoretical guarantees to our setting. Furthermore, we provide an efficient optimization algorith…

Cross-Domain Sparse Coding

Sparse coding has shown its power as an effective data representation method. However, up to now, all the sparse coding approaches are limited within the single domain learning problem. In this paper, we extend the sparse coding to cross domain learning problem, which tries to learn from a source domain to a target domain with significant different distribution. We impose the Maximum Mean Discrepancy (MMD) criterion to reduce the cross-domain distribution difference of sparse codes, and also regularize the sparse codes by the class labels of the samples from both domains to increase the discri…

Learning step sizes for unfolded sparse coding

Sparse coding is typically solved by iterative optimization techniques, such as the Iterative Shrinkage-Thresholding Algorithm (ISTA). Unfolding and learning weights of ISTA using neural networks is a practical way to accelerate estimation. In this paper, we study the selection of adapted step sizes for ISTA. We show that a simple step size strategy can improve the convergence rate of ISTA by leveraging the sparsity of the iterates. However, it is impractical in most large-scale applications. Therefore, we propose a network architecture where only the step sizes of ISTA are learned. We demonst…

Convex Coding

Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to simultaneously represent a sequence of data-vectors sparsely (i.e. sparse approximation (Tropp et al., 2006)) in terms of a 'code' defined by a set of basis elements, while also finding a code that enables such an approximation. As existing alternating optimization procedures for sparse coding are theoretically prone to severe local minima problems, we propose a conv…

Sparse Separable Nonnegative Matrix Factorization

We propose a new variant of nonnegative matrix factorization (NMF), combining separability and sparsity assumptions. Separability requires that the columns of the first NMF factor are equal to columns of the input matrix, while sparsity requires that the columns of the second NMF factor are sparse. We call this variant sparse separable NMF (SSNMF), which we prove to be NP-complete, as opposed to separable NMF which can be solved in polynomial time. The main motivation to consider this new model is to handle underdetermined blind source separation problems, such as multispectral image unmixing.…

Recklessly Approximate Sparse Coding

It has recently been observed that certain extremely simple feature encoding techniques are able to achieve state of the art performance on several standard image classification benchmarks including deep belief networks, convolutional nets, factored RBMs, mcRBMs, convolutional RBMs, sparse autoencoders and several others. Moreover, these "triangle" or "soft threshold" encodings are ex- tremely efficient to compute. Several intuitive arguments have been put forward to explain this remarkable performance, yet no mathematical justification has been offered. The main result of this report is to sh…

ProSper -- A Python Library for Probabilistic Sparse Coding with Non-Standard Priors and Superpositions

ProSper is a python library containing probabilistic algorithms to learn dictionaries. Given a set of data points, the implemented algorithms seek to learn the elementary components that have generated the data. The library widens the scope of dictionary learning approaches beyond implementations of standard approaches such as ICA, NMF or standard L1 sparse coding. The implemented algorithms are especially well-suited in cases when data consist of components that combine non-linearly and/or for data requiring flexible prior distributions. Furthermore, the implemented algorithms go beyond stand…

Approximate Method of Variational Bayesian Matrix Factorization/Completion with Sparse Prior

We derive analytical expression of matrix factorization/completion solution by variational Bayes method, under the assumption that observed matrix is originally the product of low-rank dense and sparse matrices with additive noise. We assume the prior of sparse matrix is Laplace distribution by taking matrix sparsity into consideration. Then we use several approximations for derivation of matrix factorization/completion solution. By our solution, we also numerically evaluate the performance of sparse matrix reconstruction in matrix factorization, and completion of missing matrix element in mat…

Simple, Efficient, and Neural Algorithms for Sparse Coding

Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard formulation is as a non-convex optimization problem which is solved in practice by heuristics based on alternating minimization. Re- cent work has resulted in several algorithms for sparse coding with provable guarantees, but somewhat surprisingly these are outperformed by the simple alternating minimization heuristics. Here we give a general framework for understan…

Non-negative matrix factorization with sparseness constraints

Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in parts-based representations. In this paper, we show how explicitly incorporating the notion of `sparseness' improves the found decompositions. Additionally, we provide complete MATLAB code both for standard NMF and for our extension. Our hope is that this will further the application of these methods to solving novel data-analysis problems.

快速并行随机算法用于具有KL散度的非负矩阵分解以处理大规模稀疏数据集

Fast Parallel Randomized Algorithm for Nonnegative Matrix Factorization with KL Divergence for Large Sparse Datasets

本文提出一种快速并行随机坐标下降算法，用于大规模稀疏数据集的非负矩阵分解与KL散度优化，实现更高效的稀疏建模与表示。

Robust Compressed Sensing and Sparse Coding with the Difference Map

In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$, of elements from an overcomplete dictionary. While many algorithms are competitive at both problems when $x$ is very sparse, it can be challenging to recover $x$ when it is less sparse. We present the Difference Map, which excels at sparse recovery when sparseness is lower and noise is higher. The Difference Map out-performs the state of the art with recons…

Identifiability in Two-Layer Sparse Matrix Factorization

Sparse matrix factorization is the problem of approximating a matrix $\mathbf{Z}$ by a product of $J$ sparse factors $\mathbf{X}^{(J)} \mathbf{X}^{(J-1)} \ldots \mathbf{X}^{(1)}$. This paper focuses on identifiability issues that appear in this problem, in view of better understanding under which sparsity constraints the problem is well-posed. We give conditions under which the problem of factorizing a matrix into \emph{two} sparse factors admits a unique solution, up to unavoidable permutation and scaling equivalences. Our general framework considers an arbitrary family of prescribed sparsity…

Classifiers Based on Deep Sparse Coding Architectures are Robust to Deep Learning Transferable Examples

Although deep learning has shown great success in recent years, researchers have discovered a critical flaw where small, imperceptible changes in the input to the system can drastically change the output classification. These attacks are exploitable in nearly all of the existing deep learning classification frameworks. However, the susceptibility of deep sparse coding models to adversarial examples has not been examined. Here, we show that classifiers based on a deep sparse coding model whose classification accuracy is competitive with a variety of deep neural network models are robust to adve…

Tight convex relaxations for sparse matrix factorization

Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple factors, subspace clustering and low-rank sparse bilinear regression as potential applications. We compute slow rates and an upper bound on the statistical dimension of the suggested norm for rank 1 matrices, showing that its statistical dimension is an order of magnitude smaller than the usual $\ell\_1$-norm, trace norm and their combinations. Even though our c…

Non-Negative Local Sparse Coding for Subspace Clustering

Subspace sparse coding (SSC) algorithms have proven to be beneficial to clustering problems. They provide an alternative data representation in which the underlying structure of the clusters can be better captured. However, most of the research in this area is mainly focused on enhancing the sparse coding part of the problem. In contrast, we introduce a novel objective term in our proposed SSC framework which focuses on the separability of data points in the coding space. We also provide mathematical insights into how this local-separability term improves the clustering result of the SSC frame…

Learned Interpretable Residual Extragradient ISTA for Sparse Coding

Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has attracted increasing attentions. A large number of experiments as well as some theories have proved the high efficiency of LISTA for solving sparse coding problems. However, existing LISTA methods are all serial connection. To address this issue, we propose a novel extragradient based LISTA (ELISTA), which has a residual structure and theoretical guarantees. In particular, our algorithm can also provide the interpretability for Res-Net to a certain extent. From a theoretical perspective, we prove that our met…

Supervised Dictionary Learning by a Variational Bayesian Group Sparse Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) with group sparsity constraints is formulated as a probabilistic graphical model and, assuming some observed data have been generated by the model, a feasible variational Bayesian algorithm is derived for learning model parameters. When used in a supervised learning scenario, NMF is most often utilized as an unsupervised feature extractor followed by classification in the obtained feature subspace. Having mapped the class labels to a more general concept of groups which underlie sparsity of the coefficients, what the proposed group sparse NMF model allows…

SparseCodePicking: feature extraction in mass spectrometry using sparse coding algorithms

Mass spectrometry (MS) is an important technique for chemical profiling which calculates for a sample a high dimensional histogram-like spectrum. A crucial step of MS data processing is the peak picking which selects peaks containing information about molecules with high concentrations which are of interest in an MS investigation. We present a new procedure of the peak picking based on a sparse coding algorithm. Given a set of spectra of different classes, i.e. with different positions and heights of the peaks, this procedure can extract peaks by means of unsupervised learning. Instead of an $…

FastSTMF: Efficient tropical matrix factorization algorithm for sparse data

Matrix factorization, one of the most popular methods in machine learning, has recently benefited from introducing non-linearity in prediction tasks using tropical semiring. The non-linearity enables a better fit to extreme values and distributions, thus discovering high-variance patterns that differ from those found by standard linear algebra. However, the optimization process of various tropical matrix factorization methods is slow. In our work, we propose a new method FastSTMF based on Sparse Tropical Matrix Factorization (STMF), which introduces a novel strategy for updating factor matrice…

Log-based Sparse Nonnegative Matrix Factorization for Data Representation

Nonnegative matrix factorization (NMF) has been widely studied in recent years due to its effectiveness in representing nonnegative data with parts-based representations. For NMF, a sparser solution implies better parts-based representation.However, current NMF methods do not always generate sparse solutions.In this paper, we propose a new NMF method with log-norm imposed on the factor matrices to enhance the sparseness.Moreover, we propose a novel column-wisely sparse norm, named $\ell_{2,\log}$-(pseudo) norm to enhance the robustness of the proposed method.The $\ell_{2,\log}$-(pseudo) norm i…

Efficient Identification of Butterfly Sparse Matrix Factorizations

Fast transforms correspond to factorizations of the form $\mathbf{Z} = \mathbf{X}^{(1)} \ldots \mathbf{X}^{(J)}$, where each factor $ \mathbf{X}^{(\ell)}$ is sparse and possibly structured. This paper investigates essential uniqueness of such factorizations, i.e., uniqueness up to unavoidable scaling ambiguities. Our main contribution is to prove that any $N \times N$ matrix having the so-called butterfly structure admits an essentially unique factorization into $J$ butterfly factors (where $N = 2^{J}$), and that the factors can be recovered by a hierarchical factorization method, which consis…

Dropout Training of Matrix Factorization and Autoencoder for Link Prediction in Sparse Graphs

Matrix factorization (MF) and Autoencoder (AE) are among the most successful approaches of unsupervised learning. While MF based models have been extensively exploited in the graph modeling and link prediction literature, the AE family has not gained much attention. In this paper we investigate both MF and AE's application to the link prediction problem in sparse graphs. We show the connection between AE and MF from the perspective of multiview learning, and further propose MF+AE: a model training MF and AE jointly with shared parameters. We apply dropout to training both the MF and AE parts, …

Convex Sparse Matrix Factorizations

We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rank-reducing term similar to the trace norm. In particular, our formulation introduces an explicit trade-off between size and sparsity of the decomposition of rectangular matrices. Using a large set of synthetic examples, we compare the estimation abilities of the convex and non-convex approaches, showing that while the convex formulation has a single local minimum, this may lead in some cases to performanc…

A Greedy Approach to $\ell_{0,\infty}$ Based Convolutional Sparse Coding

Sparse coding techniques for image processing traditionally rely on a processing of small overlapping patches separately followed by averaging. This has the disadvantage that the reconstructed image no longer obeys the sparsity prior used in the processing. For this purpose convolutional sparse coding has been introduced, where a shift-invariant dictionary is used and the sparsity of the recovered image is maintained. Most such strategies target the $\ell_0$ "norm" or the $\ell_1$ norm of the whole image, which may create an imbalanced sparsity across various regions in the image. In order to …

Quantum Sparse Coding

The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with an approximation method, such as lasso or orthogonal matching pursuit, thus trading off accuracy for less computational complexity. In this paper, we develop a quantum-inspired algorithm for sparse coding, with the premise that the emergence of quantum computers and Ising machines can potentially lead to more accurate estimations compared to classical approx…

Closed-form EM for Sparse Coding and its Application to Source Separation

We define and discuss the first sparse coding algorithm based on closed-form EM updates and continuous latent variables. The underlying generative model consists of a standard `spike-and-slab' prior and a Gaussian noise model. Closed-form solutions for E- and M-step equations are derived by generalizing probabilistic PCA. The resulting EM algorithm can take all modes of a potentially multi-modal posterior into account. The computational cost of the algorithm scales exponentially with the number of hidden dimensions. However, with current computational resources, it is still possible to efficie…

Universal Regularizers For Robust Sparse Coding and Modeling

Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many signal and image processing tasks. It is now well understood that the choice of the sparsity regularization term is critical in the success of such models. Based on a codelength minimization interpretation of sparse coding, and using tools from universal coding theory, we propose a framework for designing sparsity regularization terms which have theoretical and …

弥合稀疏矩阵重排与分解之间的差距：一种用于填充减少的深度学习框架

Bridging the Gap between Sparse Matrix Reordering and Factorization: A Deep Learning Framework for Fill-in Reduction

本文提出一种深度学习框架，通过谱嵌入最小化填充代理函数，弥合稀疏矩阵重排与分解之间的差距，实验表明其性能优于传统图论算法和深度学习方法。

Sparse Nonnegative Tensor Factorization and Completion with Noisy Observations

In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the tensor-tensor product of one sparse nonnegative tensor and one nonnegative tensor. We propose to minimize the sum of the maximum likelihood estimation for the observations with nonnegativity constraints and the tensor $\ell_0$ norm for the sparse factor. We show that the error bounds of the estimator of the proposed model can be established under general noise o…

Model-based Sparse Coding beyond Gaussian Independent Model

Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC) method is proposed to provide an effective and flexible framework for learning features from different data types: continuous, discrete, or categorical, and modeling different types of correlations: spatial or temporal. The specification of the sparsity level and how to adapt the estimation method to large-scale studies are also addressed. A fast EM algorithm is …

Sparse coding and dictionary learning based on the MDL principle

The power of sparse signal coding with learned dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical properties of these models, such as underfitting or overfitting given sets of data, are still not well characterized in the literature. This work aims at filling this gap by means of the Minimum Description Length (MDL) principle -- a well established information-theoretic approach to statistical inference. The resulting framework derives a family of efficient sparse coding and m…

A global optimization algorithm for sparse mixed membership matrix factorization

Mixed membership factorization is a popular approach for analyzing data sets that have within-sample heterogeneity. In recent years, several algorithms have been developed for mixed membership matrix factorization, but they only guarantee estimates from a local optimum. Here, we derive a global optimization (GOP) algorithm that provides a guaranteed $ε$-global optimum for a sparse mixed membership matrix factorization problem. We test the algorithm on simulated data and find the algorithm always bounds the global optimum across random initializations and explores multiple modes efficiently.

Bayesian Beta-Bernoulli Process Sparse Coding with Deep Neural Networks

Several approximate inference methods have been proposed for deep discrete latent variable models. However, non-parametric methods which have previously been successfully employed for classical sparse coding models have largely been unexplored in the context of deep models. We propose a non-parametric iterative algorithm for learning discrete latent representations in such deep models. Additionally, to learn scale invariant discrete features, we propose local data scaling variables. Lastly, to encourage sparsity in our representations, we propose a Beta-Bernoulli process prior on the latent fa…

Sparse Topical Coding

We present sparse topical coding (STC), a non-probabilistic formulation of topic models for discovering latent representations of large collections of data. Unlike probabilistic topic models, STC relaxes the normalization constraint of admixture proportions and the constraint of defining a normalized likelihood function. Such relaxations make STC amenable to: 1) directly control the sparsity of inferred representations by using sparsity-inducing regularizers; 2) be seamlessly integrated with a convex error function (e.g., SVM hinge loss) for supervised learning; and 3) be efficiently learned w…

深度权重分解：通过人工对称性的视角实现稀疏学习

Deep Weight Factorization: Sparse Learning Through the Lens of Artificial Symmetries

本文提出深度权重分解方法，将权重分解为多个因子并施加可微L2正则化，理论上等价于非凸稀疏正则化，并通过定制初始化和学习率策略在多种架构与数据集上优于浅层分解和剪枝方法。