Matrix concentration inequalities via the method of exchangeable pairs
Matrix concentration inequalities via the method of exchangeable pairs
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DOI：
10.1214/13-aop892
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发表时间：
2012-01
影响因子：
2.3
通讯作者：
Lester W. Mackey;Michael I. Jordan;Richard Y. Chen;Brendan Farrell;J. Tropp
中科院分区：
文献类型：
--
作者：
Lester W. Mackey;Michael I. Jordan;Richard Y. Chen;Brendan Farrell;J. Tropp
本文给出了随机矩阵谱范数的指数集中不等式和多项式矩不等式。分析需要一个矩阵扩展的标量浓度理论开发的Sourav Chatterjee使用斯坦的方法交换对。当应用到一个独立的随机矩阵的总和，这种方法产生的经典不等式由于Hoeffding，伯恩斯坦，Khintchine和罗森塔尔矩阵推广。同样的技术提供了依赖随机矩阵和依赖随机变量的更一般的矩阵值函数的和的界。
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.