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Poster
A Nonconvex Optimization Framework for Low Rank Matrix Estimation
Tuo Zhao · Zhaoran Wang · Han Liu

Mon Dec 07 04:00 PM -- 08:59 PM (PST) @ 210 C #101
in Poster Session »

We study the estimation of low rank matrices via nonconvex optimization. Compared with convex relaxation, nonconvex optimization exhibits superior empirical performance for large scale instances of low rank matrix estimation. However, the understanding of its theoretical guarantees are limited. In this paper, we define the notion of projected oracle divergence based on which we establish sufficient conditions for the success of nonconvex optimization. We illustrate the consequences of this general framework for matrix sensing and completion. In particular, we prove that a broad class of nonconvex optimization algorithms, including alternating minimization and gradient-type methods, geometrically converge to the global optimum and exactly recover the true low rank matrices under standard conditions.

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Author Information

Tuo Zhao (Johns Hopkins University Princeton University)
Zhaoran Wang (Princeton University)
Han Liu (Princeton University)

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