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Matrix Concentration Inequalities via the Method of Exchangeable Pairs

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I will present an approach to deriving exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix based on Stein’s method of exchangeable pairs. Our work extends results by Chatterjee on concentration for scalar random variables to the setting of random matrices. 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.

This talk is part of the Machine Learning @ CUED series.

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