LSV-Based Tail Inequalities for Sums of Random Matrices
- 论文类型：期刊论文
- 第一作者：Zhang, Chao
- 通讯作者：Zhang, C (reprint author), Dalian Univ Technol, Sch Math Sci, Dalian 116024, Liaoning, Peoples R China.
- 合写作者：Du, Lei,Tao, Dacheng
- 发表刊物：NEURAL COMPUTATION
- 收录刊物：SCIE、EI、PubMed、Scopus
- 卷号：29
- 期号：1
- 页面范围：247-262
- ISSN号：0899-7667
- 摘要：The techniques of random matrices have played an important role in many machine learning models. In this letter, we present a new method to study the tail inequalities for sums of random matrices. Different from other work (Ahlswede & Winter, 2002; Tropp, 2012; Hsu, Kakade, & Zhang, 2012), our tail results are based on the largest singular value (LSV) and independent of the matrix dimension. Since the LSV operation and the expectation are noncommutative, we introduce a diagonalization method to convert the LSV operation into the trace operation of an infinitely dimensional diagonal matrix. In this way, we obtain another version of Laplace-transform bounds and then achieve the LSV-based tail inequalities for sums of random matrices.
- 发表时间：2017-01-01