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Matrix Denoising with Weighted Loss

Mathematics of Data & Decisions

Speaker: Will Leeb, University of Minnesota
Related Webpage: http://www-users.math.umn.edu/~wleeb/
Location: 1147 MSB
Start time: Tue, Mar 10 2020, 4:10PM

This talk 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 a variety of problems, such as heteroscedastic noise, missing data, and submatrix estimation. We introduce a family of spectral denoisers, which preserve the left and right singular subspaces of the observed matrix. Using new asymptotic results on the spiked covariance model in high dimensions, we derive the optimal spectral denoiser for weighted loss. We demonstrate the behavior of our method through numerical simulations.