Emergent Mind
Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach
(1609.03240)
Published Sep 12, 2016
in
stat.ML
,
cs.IT
,
cs.LG
,
math.IT
,
math.NA
,
and
math.OC
Abstract
We consider the non-square matrix sensing problem, under restricted isometry property (RIP) assumptions. We focus on the non-convex formulation, where any rank-$r$ matrix $X \in \mathbb{R}{m \times n}$ is represented as $UV\top$, where $U \in \mathbb{R}{m \times r}$ and $V \in \mathbb{R}{n \times r}$. In this paper, we complement recent findings on the non-convex geometry of the analogous PSD setting [5], and show that matrix factorization does not introduce any spurious local minima, under RIP.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.