Noisy low-rank matrix completion with general sampling distribution

Olga Klopp

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Noisy low-rank matrix completion with general sampling distribution

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arxiv 1203.0108 v3 pith:J5SXVAY2 submitted 2012-03-01 math.ST stat.TH

Noisy low-rank matrix completion with general sampling distribution

Olga Klopp This is my paper

classification math.ST stat.TH

keywords completionconsiderdistributiongeneralmatrixnoiseperformancesampling

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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.

Noisy low-rank matrix completion with general sampling distribution

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