Open Access
November 2019 Structured matrix estimation and completion
Olga Klopp, Yu Lu, Alexandre B. Tsybakov, Harrison H. Zhou
Bernoulli 25(4B): 3883-3911 (November 2019). DOI: 10.3150/19-BEJ1114


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 establish 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. "Structured matrix estimation and completion." Bernoulli 25 (4B) 3883 - 3911, November 2019.


Received: 1 September 2017; Revised: 1 February 2019; Published: November 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07110159
MathSciNet: MR4010976
Digital Object Identifier: 10.3150/19-BEJ1114

Keywords: Matrix completion , matrix estimation , Minimax optimality , mixture model , Stochastic block model

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 4B • November 2019
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