The Statistics Seminar speaker for Wednesday, April 28, 2021, is Jonathan Niles-Weed, 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.
Talk: Matrix concentration for products and the streaming k-PCA problem
Zoom link to be sent to SDS list servs
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. Based on joint work with Huang, Tropp, and Ward.