Subadditivity of Matrix phi-Entropy and Concentration of Random Matrices

TL;DR

This paper introduces a matrix extension of the entropy method to derive concentration inequalities for random matrices, offering a novel approach that parallels classical scalar techniques.

Contribution

It develops a new matrix entropy method and applies it to establish matrix concentration inequalities, advancing the theoretical toolkit for analyzing random matrices.

Findings

Derived new matrix concentration inequalities

Extended entropy method to matrix setting

Provided theoretical bounds for spectral norms

Abstract

Matrix concentration inequalities provide a direct way to bound the typical spectral norm of a random matrix. The methods for establishing these results often parallel classical arguments, such as the Laplace transform method. This work develops a matrix extension of the entropy method, and it applies these ideas to obtain some matrix concentration inequalities.