New Methods for Low-Rank Matrix Denoising

William Leeb, University of Minnesota
Event time: 
Wednesday, December 15, 2021 - 2:30pm
Location: See map
Event description: 

Abstract: In this talk, I will describe a new class of methods for estimating a low-rank matrix from a noisy observed matrix, where the error is measured by a type of weighted loss function. Such loss functions arise naturally in problems such as submatrix denoising, heteroscedastic noise filtering, and estimation with missing data. I will introduce a family of spectral denoisers, which preserve the left and right singular subspaces of the observed matrix. I will also show how denoising with weighted loss yields a new approach to unweighted denoising that is asymptotically at least as good as singular value shrinkage, and can perform better when the matrix is heterogeneous. I will demonstrate the behavior of the method through numerical simulations.

Event Type: 
Applied Mathematics