Non-Square Matrix Sensing Without Spurious Local Minima via the Burer-Monteiro Approach
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.
Cite
Text
Park et al. "Non-Square Matrix Sensing Without Spurious Local Minima via the Burer-Monteiro Approach." International Conference on Artificial Intelligence and Statistics, 2017.Markdown
[Park et al. "Non-Square Matrix Sensing Without Spurious Local Minima via the Burer-Monteiro Approach." International Conference on Artificial Intelligence and Statistics, 2017.](https://mlanthology.org/aistats/2017/park2017aistats-non/)BibTeX
@inproceedings{park2017aistats-non,
title = {{Non-Square Matrix Sensing Without Spurious Local Minima via the Burer-Monteiro Approach}},
author = {Park, Dohyung and Kyrillidis, Anastasios and Caramanis, Constantine and Sanghavi, Sujay},
booktitle = {International Conference on Artificial Intelligence and Statistics},
year = {2017},
pages = {65-74},
url = {https://mlanthology.org/aistats/2017/park2017aistats-non/}
}