Related papers: A Note on Sparse Supersaturation and Extremal Resu…
The aim of the paper is twofold. We establish refined Strichartz estimates for the Schr\"odinger equation on tori within the framework of partial regularity. As a result, we reveal that the solution of the free Schr\"odinger equation has…
This paper studies the hierarchy of sparse matrix Moment-SOS relaxations for solving sparse polynomial optimization problems with matrix constraints. First, we prove a sufficient and necessary condition for the sparse hierarchy to be tight.…
Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result that characterizes properties of an exponential system on a…
Inspired by Kalikow-type decompositions, we introduce a new stochastic model of infinite neuronal networks, for which we establish sharp oracle inequalities for Lasso methods and restricted eigenvalue properties for the associated Gram…
We compute spectra of large stochastic matrices $W$, defined on sparse random graphs, where edges $(i,j)$ of the graph are given positive random weights $W_{ij}>0$ in such a fashion that column sums are normalized to one. We compute spectra…
The abstract model of stochastic probing was presented by Gupta and Nagarajan (IPCO'13), and provides a unified view of a number of problems. Adamczyk, Sviridenko, Ward (STACS'14) gave better approximation for matroid environments and…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
Let $H=(V,E)$ be an edge-weighted hypergraph of rank $r$. Kogan and Krauthgamer extended Bencz\'{u}r and Karger's random sampling scheme for cut sparsification from graphs to hypergraphs. The sampling requires an algorithm for computing the…
We show that the sequential closure of a family of probability measures on the canonical space of c{\`a}dl{\`a}g paths satisfying Stricker's uniform tightness condition is a weak${}^*$ compact set of semimartingale measures in the pairing…
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…
Relationship inference from sparse data is an important task with applications ranging from product recommendation to drug discovery. A recently proposed linear model for sparse matrix completion has demonstrated surprising advantage in…
We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
This paper develops alternative hyperparameters for specifying sparse Recurrent Neural Networks (RNNs). These hyperparameters allow for varying sparsity within the trainable weight matrices of the model while improving overall performance.…
Recent results in compressed sensing show that, under certain conditions, the sparsest solution to an underdetermined set of linear equations can be recovered by solving a linear program. These results either rely on computing sparse…
This work derives upper bounds on the convergence rate of the moment-sum-of-squares hierarchy with correlative sparsity for global minimization of polynomials on compact basic semialgebraic sets. The main conclusion is that both sparse…
This paper proposes a verification method for sparse linear systems $Ax=b$ with general and nonsingular coefficients. A verification method produces the error bound for a given approximate solution. Conventional methods use one of two…
We study high-dimensional least-squares regression within a subgaussian statistical learning framework with heterogeneous noise. It includes $s$-sparse and $r$-low-rank least-squares regression when a fraction $\epsilon$ of the labels are…
The purpose of this paper is to extend a result by Donoho and Huo, Elad and Bruckstein, Gribnoval and Nielsen on sparse representations of signals in dictionaries to general matrices. We consider a general fixed measurement matrix, not…
We introduce a new notion of sparsification, called \emph{strong sparsification}, in which constraints are not removed but variables can be merged. As our main result, we present a strong sparsification algorithm for 1-in-3-SAT. The…