← List all talks ...

Fundamental limits of low-rank matrix estimation with diverging aspect ratios

Yuchen Wu – PhD student, Stanford

Thu, 1-Dec-2022 / 4:00pm / Packard 202

Abstract

In this talk, I will present results on estimating the factors of a low-rank n×d matrix, when this is corrupted by additive Gaussian noise. A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known) covariances. Simple spectral methods do not take into account the distribution of the entries of these factors and are therefore often suboptimal. This talk characterizes the asymptotics of the minimum estimation error under the assumption that the distribution of the entries is known to the statistician.

Our results apply to the high-dimensional regime n,d→∞ and d/n→∞ (or d/n→0) and generalize earlier work that focused on the proportional asymptotics n,d→∞, d/n→δ∈(0,∞). We outline an interesting signal strength regime in which d/n→∞and partial recovery is possible for the left singular vectors while impossible for the right singular vectors.

I will illustrate the general theory by deriving consequences for Gaussian mixture clustering and carrying out a numerical study on genomics data.

Bio

Yuchen Wu is a fifth-year PhD student in the Department of Statistics at Stanford University, advised by Professor Andrea Montanari. Prior to Stanford, she received her bachelor’s degree in mathematics from Tsinghua University. Her research interests include high-dimensional statistics, theory of deep learning, optimization and sampling.