Statistics Department Seminar Series: Joel Tropp, PhD, Cal Tech

Joel Tropp, PhD

Professor of Applied & Computational Mathematics

California Institute of Technology

‘Sketchy Decisions: Low-rank Matrix Optimization with Optimal Storage’

Abstract: Convex matrix optimization problems with low-rank solutions play a fundamental role in signal processing, statistics, and related disciplines. These problems are difficult to solve because of the cost of maintaining the matrix decision variable, even though the low-rank solution has few degrees of freedom. This talk presents the first algorithm that provably solves these problems using optimal storage. The algorithm produces high-quality solutions to large problem instances that, previously, were intractable.

Joint with Volkan Cevher, Roarke Horstmeyer, Quoc Tran-Dinh, Madeleine Udell, and Alp Yurtsever.

Bio: My research identifies situations where sparse approximation problems can be solved using efficient computational algorithms. In particular, I have analyzed the performance of greedy pursuit methods, which are popular with practitioners because of their speed. I have also developed a substantial body of results for techniques based on convex programming. A third strand of work addresses the tractability of random instances of sparse approximation. This research has yielded new results on the behavior of random matrices.

Welcome Reception at 11:00 a.m.