Related papers: Testing Sparsity over Known and Unknown Bases

We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an…

The problem of detecting the sparsity pattern of a k-sparse vector in R^n from m random noisy measurements is of interest in many areas such as system identification, denoising, pattern recognition, and compressed sensing. This paper…

We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…

We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…

This note is concerned with deterministic constructions of $m \times N$ matrices satisfying a restricted isometry property from $\ell_2$ to $\ell_1$ on $s$-sparse vectors. Similarly to the standard ($\ell_2$ to $\ell_2$) restricted isometry…

A sparsity pattern in $\mathbb{R}^{n \times m}$, for $m\geq n$, is a vector subspace of matrices admitting a basis consisting of canonical basis vectors in $\mathbb{R}^{n \times m}$. We represent a sparsity pattern by a matrix with…

We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with $k$ $>>$ $n$ regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension…

A matrix $A$ is said to have the $\ell_p$-Restricted Isometry Property ($\ell_p$-RIP) if for all vectors $x$ of up to some sparsity $k$, $\|{Ax}\|_p$ is roughly proportional to $\|{x}\|_p$. We study this property for $m \times n$ matrices…

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…

We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…

A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as a measure of inherent diversity, of different network parameters. It utilizes sparsity index…

We present a Bayesian approach to identify optimal transformations that map model input points to low dimensional latent variables. The "projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to…

We introduce a \emph{batch} version of sparse recovery, where the goal is to report a sequence of vectors $A_1',\ldots,A_m' \in \mathbb{R}^n$ that estimate unknown signals $A_1,\ldots,A_m \in \mathbb{R}^n$ using a few linear measurements,…

In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…

Although sparse neural networks have been studied extensively, the focus has been primarily on accuracy. In this work, we focus instead on network structure, and analyze three popular algorithms. We first measure performance when structure…

We introduce a general framework for testing goodness-of-fit for Gaussian graphical models in both the low- and high-dimensional settings. This framework is based on a novel algorithm for generating exchangeable copies by conditioning on…

In group testing, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether any defective item is present. This problem is relevant in areas such as medical testing, data…

Randomized matrix sparsification has proven to be a fruitful technique for producing faster algorithms in applications ranging from graph partitioning to semidefinite programming. In the decade or so of research into this technique, the…

Sparse random projection (RP) is a popular tool for dimensionality reduction that shows promising performance with low computational complexity. However, in the existing sparse RP matrices, the positions of non-zero entries are usually…

Given an $n*n$ sparse symmetric matrix with $m$ nonzero entries, performing Gaussian elimination may turn some zeroes into nonzero values. To maintain the matrix sparse, we would like to minimize the number $k$ of these changes, hence…