Nonsquare matrix sensing without spurious local minima via the BurerMonteiro approach
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Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:6574, 2017.
Abstract
We consider the nonsquare matrix sensing problem, under restricted isometry property (RIP) assumptions. We focus on the nonconvex formulation, where any rankr 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 nonconvex geometry of the analogous PSD setting [5], and show that matrix factorization does not introduce any spurious local minima, under RIP.
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