MATRIX CONCENTRATION INEQUALITIES VIA THE METHOD OF EXCHANGEABLE PAIRS

• 成果类型: Article
• 署名作者: Mackey, Lester; Jordan, Michael I.; Chen, Richard Y.; Farrell, Brendan; Tropp, Joel A.
• 署名单位: Stanford University; University of California System; University of California Berkeley; University of California System; University of California Berkeley; California Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP892
• 发表日期: 2014
• 页码: 906-945
• 关键词: sums; khintchine

摘要

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.