Van Trees inequality, group equivariance, and estimation of principal subspaces

TL;DR

This paper derives non-asymptotic lower bounds for estimating principal subspaces, providing new insights into the excess risk in PCA and matrix denoising problems.

Contribution

It introduces novel non-asymptotic bounds for principal subspace estimation, connecting Van Trees inequality and group equivariance.

Findings

New non-asymptotic lower bounds for principal subspace estimation

Improved understanding of excess risk in PCA

Applications to matrix denoising problem

Abstract

We establish non-asymptotic lower bounds for the estimation of principal subspaces. As applications, we obtain new results for the excess risk of principal component analysis and the matrix denoising problem.