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Noisy Low-rank Matrix Completion with General Sampling Distribution

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  • Olga Klopp

    (CREST)

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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  • Olga Klopp, 2012. "Noisy Low-rank Matrix Completion with General Sampling Distribution," Working Papers 2012-06, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2012-06
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    References listed on IDEAS

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    1. Angelika Rohde & Alexandre Tsybakov, 2010. "Estimation on High-dimensional Low Rank Matrices," Working Papers 2010-25, Center for Research in Economics and Statistics.
    2. A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
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    Cited by:

    1. Olga Klopp & Alexandre Tsybakov, 2016. "Estimation of matrices with row sparsity," Working Papers 2016-11, Center for Research in Economics and Statistics.

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