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Activity Number: 314 - Recent Advances in High-Dimensional Inferences
Type: Invited
Date/Time: Tuesday, August 1, 2017 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #322034
Title: Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Data Analysis
Author(s): Tony Cai* and Anru Zhang
Companies: University of Pennsylvania and University of Wisconsin-Madison
Keywords: clustering ; high-dimensional statistics ; perturbation bound ; singular value decomposition ; spectral method

Perturbation bounds for singular spaces, in particular Wedin's $\sin \Theta$ theorem, are a fundamental tool in many fields including high-dimensional statistics, machine learning, and applied mathematics. In this talk, we present new and separate perturbation bounds, measured in both spectral and Frobenius $\sin \Theta$ distances, for the left and right singular subspaces. Lower bounds, which show that the individual perturbation bounds are rate-optimal, are also given. The new perturbation bounds are applicable to a wide range of problems. We will discuss applications to low-rank matrix denoising and singular space estimation, high-dimensional clustering, and canonical correlation analysis (CCA).

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

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