Probability Seminar

Date: March 31, 2021

Time: 2:00PM - 3:00PM

Location: Zoom

Speaker: Jonathan Niles-Weed, Courant Institute of Mathematical Sciences

Title: Matrix concentration for products and the streaming k-PCA problem

Abstract: We develop nonasymptotic concentration bounds for products of independent random matrices. Our bounds exactly match those available for scalar random variables and continue the program, initiated by Ahlswede-Winter, Oliveira, and Tropp, of extending familiar concentration bounds to the noncommutative setting. The argument relies on the optimal uniform smoothness properties of the Schatten trace class. We apply our results to analyze a non-convex stochastic descent algorithm for streaming PCA due to Erkki Oja. Despite its simplicity, this algorithm has resisted optimal analysis outside of the rank-one case.