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Noisy low-rank matrix completion with general sampling distribution

Klopp, Olga (2014), Noisy low-rank matrix completion with general sampling distribution, Bernoulli, 20, 1, p. 1-393. http://dx.doi.org/10.3150/12-BEJ486

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00675413
Date
2014
Journal name
Bernoulli
Volume
20
Number
1
Publisher
Bernoulli Society for Mathematical Statistics and Probability
Pages
1-393
Publication identifier
Metadata
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Author(s)
Klopp, Olga
Abstract (EN)
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.
Subjects / Keywords
high-dimensional sparse model; unknown variance; low rank matrix estimation; matrix completion