Published: Oct. 28, 2016
Event Description:
Sean O'Rourke, Department of Mathematics, University of ÃÛÌÇÖ±²¥ Boulder

Singular values and vectors under random perturbation

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. 

Time permitting, I will also discuss some applications of these bounds to community detection and matrix recovery type problems.  This talk is based on joint work with Van Vu and Ke Wang.

Location Information:
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1111 Engineering DR
Boulder, CO
¸é´Ç´Ç³¾:Ìý245
Contact Information:
Name: Ian Cunningham
Phone: 303-492-4668
Email: amassist@colorado.edu