| Event Description: Sean O'Rourke, Department of Mathematics, University of Colorado 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: ÌýÌý() 1111 Engineering DR Boulder, CO ¸é´Ç´Ç³¾:Ìý245 |
| Contact Information: Name: Ian Cunningham Phone: 303-492-4668 Email: amassist@colorado.edu |