On the Absence of Spurious Local Minima in Nonlinear Low-Rank Matrix Recovery Problems
Abstract
The restricted isometry property (RIP) is a well-known condition that guarantees the absence of spurious local minima in low-rank matrix recovery problems with linear measurements. In this paper, we introduce a novel property named bound difference property (BDP) to study low-rank matrix recovery problems with nonlinear measurements. Using RIP and BDP jointly, we propose a new criterion to certify the nonexistence of spurious local minima in the rank-1 case, and prove that it leads to a much stronger theoretical guarantee than the existing bounds on RIP.
Cite
Text
Bi and Lavaei. "On the Absence of Spurious Local Minima in Nonlinear Low-Rank Matrix Recovery Problems." Artificial Intelligence and Statistics, 2021.Markdown
[Bi and Lavaei. "On the Absence of Spurious Local Minima in Nonlinear Low-Rank Matrix Recovery Problems." Artificial Intelligence and Statistics, 2021.](https://mlanthology.org/aistats/2021/bi2021aistats-absence/)BibTeX
@inproceedings{bi2021aistats-absence,
title = {{On the Absence of Spurious Local Minima in Nonlinear Low-Rank Matrix Recovery Problems}},
author = {Bi, Yingjie and Lavaei, Javad},
booktitle = {Artificial Intelligence and Statistics},
year = {2021},
pages = {379-387},
volume = {130},
url = {https://mlanthology.org/aistats/2021/bi2021aistats-absence/}
}