Open Access
February 2014 Noisy low-rank matrix completion with general sampling distribution
Olga Klopp
Bernoulli 20(1): 282-303 (February 2014). DOI: 10.3150/12-BEJ486


In the present paper, we consider the problem of matrix completion with noise. Unlike previous works, we consider quite general sampling distribution and we do not need to know or to estimate the variance of the noise. Two new nuclear-norm penalized estimators are proposed, one of them of “square-root” type. We analyse their performance under high-dimensional scaling and provide non-asymptotic bounds on the Frobenius norm error. Up to a logarithmic factor, these performance guarantees are minimax optimal in a number of circumstances.


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Olga Klopp. "Noisy low-rank matrix completion with general sampling distribution." Bernoulli 20 (1) 282 - 303, February 2014.


Published: February 2014
First available in Project Euclid: 22 January 2014

MathSciNet: MR3160583
zbMATH: 06282552
Digital Object Identifier: 10.3150/12-BEJ486

Keywords: high-dimensional sparse model , low rank matrix estimation , Matrix completion , unknown variance

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

Vol.20 • No. 1 • February 2014
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