LSV-Based Tail Inequalities for Sums of Random Matrices
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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.
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2020 ◽
Vol 2
(1)
◽
pp. 3-6
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2018 ◽
Vol 13
(1)
◽
pp. 21
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2021 ◽
2019 ◽
Vol 7
(6)
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pp. 985-990
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