Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:65-74, 2017.
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 $X ∈R^m x n$ is represented as $UV^T$, where $U ∈R^m x r$ and $V ∈R^n x r$. In this paper, we complement recent findings on the non-convex geometry of the analogous PSD setting , and show that matrix factorization does not introduce any spurious local minima, under RIP.