Online Program Home
My Program

Abstract Details

Activity Number: 42
Type: Contributed
Date/Time: Sunday, July 31, 2016 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #320742
Title: Perturbation Bound on Unilateral Singular Vectors
Author(s): Anru Zhang*
Companies: University of Wisconsin - Madison
Keywords: singular value decomposition ; spectral method ; sine-theta norm ; matrix denoising ; canonical correlation analysis
Abstract:

In many probability, statistics and machine learning applications, singular vector perturbation bound, which describes how the singular vectors change after possible perturbations to the matrices, has been widely considered. The prominent Wedin (1972)'s sine-theta law addressed this question by providing a uniform perturbation bound on both left and right singular vectors. To achieve respective better rate on one side of singular vector perturbation, in this article we propose a new perturbation bound on unilateral singular vectors. Both upper bound and lower bound results are developed for perturbation under both spectral and Frobenius sine-theta norms. The proposed technical tool is further applied to a number of problems including matrix denoising, canonical correlation analysis, where we are able to provide better results comparing to the literature. Some related problems are also briefly discussed.


Authors who are presenting talks have a * after their name.

Back to the full JSM 2016 program

 
 
Copyright © American Statistical Association