Related papers: Approximating Sparse Matrices and their Functions …
The shrinkage function is widely used in matrix low-rank approximation, compressive sensing, and statistical estimation. In this article, an elementary derivation of the shrinkage function is given. In addition, applications of the…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…
Deep neural networks with lots of parameters are typically used for large-scale computer vision tasks such as image classification. This is a result of using dense matrix multiplications and convolutions. However, sparse computations are…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition and the anchored decomposition are typical techniques to find…
We consider sparse matrix estimation where the goal is to estimate an $n\times n$ matrix from noisy observations of a small subset of its entries. We analyze the estimation error of the popularly utilized collaborative filtering algorithm…
We describe an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension. This work is an extension of the so-called Sparse Cardinal Sine…
In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has…
We propose a novel value function approximation technique for Markov decision processes. We consider the problem of compactly representing the state-action value function using a low-rank and sparse matrix model. The problem is to decompose…
This paper is concerned with the problem of approximating the determinant of A for a large sparse symmetric positive definite matrix A. It is shown that an efficient solution of this problem is obtained by using a sparse approximate inverse…
We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a…
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…
We study the problem of learning a structured approximation (low-rank, sparse, banded, etc.) to an unknown matrix $A$ given access to matrix-vector product (matvec) queries of the form $x \rightarrow Ax$ and $x \rightarrow A^Tx$. This…
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…
In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…
This is the second of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The first paper presented the original algorithm, its…
Sparse support recovery arises in many applications in communications and signal processing. Existing methods tackle sparse support recovery problems for a given measurement matrix, and cannot flexibly exploit the properties of sparsity…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…