A Note on Matrix Concentration Inequalities via the Method of Exchangeable Pairs

TL;DR

This paper improves matrix concentration inequalities using exchangeable pairs and introduces new trace inequalities for matrix exponentials, advancing theoretical tools for matrix analysis.

Contribution

It develops an improved bounded differences inequality for matrix functions and establishes new trace inequalities, enhancing the theoretical framework for matrix concentration.

Findings

Enhanced matrix concentration bounds

New trace inequalities for matrix exponential

Methodological advancements in exchangeable pairs

Abstract

The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs". Along the way, we prove new trace inequalities for the matrix exponential.