Noisy low-rank matrix completion with general sampling distribution

被引：131
作者：
Klopp, Olga [1 ,2 ]
机构：
[1] Univ Paris Quest Nanterre, MODALX, F-92001 Nanterre, France
[2] CREST, F-92001 Nanterre, France
来源：
BERNOULLI | 2014年 / 20卷 / 01期
关键词：
high-dimensional sparse model; low rank matrix estimation; matrix completion; unknown variance; PENALIZATION;
D O I：
10.3150/12-BEJ486
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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.
引用
收藏
页码：282 / 303
页数：22
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