#### Abstract Details

 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 Abstract: 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.