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Noisy low-rank matrix completion with general sampling distribution

Abstract : In the present paper we consider the problem of matrix completion with noise for general sampling schemes. Unlike previous works, in our construction we do not need to know or to evaluate the sampling distribution or the variance of the noise. We propose new nuclear-norm penalized estimators, one of them of the ''square-root'' type. We prove that, up to a logarithmic factor, our estimators achieve optimal rates with respect to the estimation error.
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https://hal.archives-ouvertes.fr/hal-00675413
Contributor : Olga Klopp <>
Submitted on : Friday, June 15, 2012 - 1:34:27 PM
Last modification on : Thursday, March 5, 2020 - 5:51:03 PM
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  • HAL Id : hal-00675413, version 2
  • ARXIV : 1203.0108

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Olga Klopp. Noisy low-rank matrix completion with general sampling distribution. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2014, 20 (1), pp.282--303. ⟨hal-00675413v2⟩

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