Matrix Concentration for Products

Abstract: We develop nonasymptotic concentration bounds for products of independent random matrices. Such products arise in the study of stochastic algorithms, linear dynamical systems, and random walks on groups. Our bounds exactly match those available for scalar random variables and continue the program, initiated by Ahlswede-Winter and Tropp, of extending familiar concentration bounds to the noncommutative setting. Our proof technique relies on geometric properties of the Schatten trace class.
Joint work with D. Huang, J. A. Tropp, and R. Ward.

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Bio: Jonathan Niles-Weed is an Assistant Professor of Mathematics and Data Science at the Courant Institute of Mathematical Sciences and the Center for Data Science at NYU, where he is a core member of the Math and Data group. He studies statistics, probability, and machine learning, and his recent work focuses data with geometry structure and on optimal transport. He received his Ph.D. in Mathematics and Statistics from MIT.