Estimation of matrices with row sparsity

TL;DR

This paper derives minimax optimal rates for estimating matrices with row sparsity from noisy data, emphasizing the importance of lower bounds in understanding the limits of such estimations.

Contribution

It provides the first comprehensive analysis of minimax rates for row-sparse matrix estimation, including the derivation of fundamental lower bounds.

Findings

Established minimax optimal convergence rates.

Derived fundamental lower bounds for estimation accuracy.

Enhanced understanding of the limits of row-sparse matrix recovery.

Abstract

An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of convergence for estimating matrices with row sparsity. A major focus in the present paper is on the derivation of lower bounds.