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发布时间：2019-03-12

论文类型：期刊论文

发表时间：2017-01-01

发表刊物：NEURAL COMPUTATION

收录刊物：Scopus、PubMed、EI、SCIE

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.