Singular values and vectors under random perturbation: theory and applications

Date(s):

Location:
Jacobs Hall, Room 2512, Jacobs School of Engineering, 9500 Gilman Dr, La Jolla, San Diego, California 92093

Sponsored By:
Professor Behrouz Touri

Speaker(s):
Sean O'Rouke
University of Colorado
Department of Mathematics
Sean O'Rouke

Abstract:

Computing the singular values and singular vectors of a large matrix is a basic task in high dimensional data analysis with many applications in computer science and statistics. In practice, however, data is often perturbed by noise. A natural question is the following. How much does a small perturbation to the matrix change the singular values and vectors? Classical (deterministic) theorems, such as those by Davis-Kahan, Wedin, and Weyl, give tight estimates for the worst-case scenario. In this talk, I will consider the case when the perturbation is random. In this setting, better estimates can be achieved when our matrix has low rank. I will also discuss several applications of these results including locating hidden structure in a random graph and the matrix completion problem.  This talk is based on joint work with Van Vu and Ke Wang.

Speaker Bio:
Sean O’Rourke is an Assistant Professor at the University of Colorado Boulder. Before joining the University of Colorado, he was a postdoctoral research associate at Yale University. Sean received his Ph.D. from the University of California, Davis in 2011 under the supervision of Alexander Soshnikov. His research interests include Probability Theory and Mathematical Physics, and he routinely studies random matrices and random polynomials.

Contact:
Wyn Hughes (whughes@eng.ucsd.edu)