Sharp Bounds for Multiple Models in Matrix Completion
Statistics Theory
2026-03-06 v4 Statistics Theory
Abstract
In this paper, we demonstrate how a class of advanced matrix concentration inequalities, introduced in \cite{brailovskaya2024universality}, can be used to eliminate the dimensional factor in the convergence rate of matrix completion. This dimensional factor represents a significant gap between the upper bound and the minimax lower bound, especially in high dimension. Through a more precise spectral norm analysis, we remove the dimensional factors for three popular matrix completion estimators, thereby establishing their minimax rate optimality.
Cite
@article{arxiv.2411.13199,
title = {Sharp Bounds for Multiple Models in Matrix Completion},
author = {Dali Liu and Haolei Weng},
journal= {arXiv preprint arXiv:2411.13199},
year = {2026}
}
Comments
37 pages. Accepted by the Electronic Journal of Statistics. All comments are warmly welcomed