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arXiv · 1707.02090

Structured Matrix Estimation and Completion

Olga Klopp·Yu Lu·Alexandre B. Tsybakov·Harrison H. Zhou
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Abstract

We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and dictionary learning. We consider the optimal convergence rates in a minimax sense for estimation of the signal matrix under the Frobenius norm and under the spectral norm. As a consequence of our general result we obtain minimax optimal rates of convergence for various special models.

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Olga Klopp, Yu Lu, Alexandre B. Tsybakov, Harrison H. Zhou. 2017-07-07. Structured Matrix Estimation and Completion. https://arxiv.org/abs/1707.02090

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