2021-03-18-bi21a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
On the Absence of Spurious Local Minima in Nonlinear Low-Rank Matrix Recovery Problems	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.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	bi21a	0	On the Absence of Spurious Local Minima in Nonlinear Low-Rank Matrix Recovery Problems	379	387	379-387	379	false	Bi, Yingjie and Lavaei, Javad	given family Yingjie Bi given family Javad Lavaei	2021-03-18		Proceedings of The 24th International Conference on Artificial Intelligence and Statistics	130	inproceedings	date-parts 2021 3 18	http://proceedings.mlr.press/v130/bi21a/bi21a.pdf	label link Supplementary PDF http://proceedings.mlr.press/v130/bi21a/bi21a-supp.pdf