Related papers: Upper-bounding $\ell_1$-optimization weak threshol…

Spark plays a great role in studying uniqueness of sparse solutions of the underdetermined linear equations. In this article, we derive a new lower bound of spark. As an application, we obtain a new criterion for the uniqueness of sparse…

We study the recovery of sparse vectors from subsampled random convolutions via $\ell_1$-minimization. We consider the setup in which both the subsampling locations as well as the generating vector are chosen at random. For a subgaussian…

The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…

The sparsity of natural signals and images in a transform domain or dictionary has been extensively exploited in several applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis…

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…

Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…

The problem of finding the sparsest solution to a linear underdetermined system of equations, often appearing, e.g., in data analysis, optimal control, system identification, or sensor selection problems, is considered. This non-convex…

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To simultaneously achieve sparsity and positive…

We give sparsity results and present algorithms for calculating minimum (vector) 1-norm universal solvers connected to least-squares problems. In particular, besides universal least-squares solvers, we consider minimum-rank universal…

In this paper we provide a complementary set of results to those we present in our companion work \cite{Stojnicl1HidParasymldp} regarding the behavior of the so-called partial $\ell_1$ (a variant of the standard $\ell_1$ heuristic often…

We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…

Two approximation algorithms are proposed for $\ell_1$-regularized sparse rank-1 approximation to higher-order tensors. The algorithms are based on multilinear relaxation and sparsification, which are easily implemented and well scalable.…

We reduce the problem of proving decay estimates for viscosity solutions of fully nonlinear PDEs to proving analogous estimates for solutions of one-dimensional ordinary differential inequalities. Our machinery allow the ellipticity to…

This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…

In many high-dimensional problems, like sparse-PCA, planted clique, or clustering, the best known algorithms with polynomial time complexity fail to reach the statistical performance provably achievable by algorithms free of computational…

We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…

This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…

This work develops a framework to discover relations between the components of the solution to a given initial-value problem for a first-order system of ordinary differential equations. This is done by using sparse identification techniques…

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

We establish the existence of weak solutions of coupled systems of elliptic partial differential equations with quasimonotone nonlinearities in the domain interior and on the boundary. When the nonlinearities satisfy some monotonicity…