Matrix concentration inequalities via the method of exchangeable pairs

Citation
Mackey, Lester et al., Matrix concentration inequalities via the method of exchangeable pairs, Annals of probability , 42(3), 2014, pp. 906-945
Journal title
ISSN journal
00911798
Volume
42
Issue
3
Year of publication
2014
Pages
906 - 945
Database
ACNP
SICI code
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.