Matrix concentration inequalities via the method of exchangeable pairs

Abstract

This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav Chatterjee using Stein's method of exchangeable pairs. When applied to a sum of independent random matrices, this approach yields matrix generalizations of the classical inequalities due to Hoeffding, Bernstein, Khintchine and Rosenthal. The same technique delivers bounds for sums of dependent random matrices and more general matrix-valued functions of dependent random variables.

Published in at http://dx.doi.org/10.1214/13-AOP892 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
• Noncommutative Bennett and Rosenthal inequalities
• The spectral norm error of the naive Nystrom extension
• Concentration-Based Guarantees for Low-Rank Matrix Reconstruction

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