Noisy Low-rank Matrix Completion with General Sampling Distribution
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
|Date of creation:||Mar 2012|
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- 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.
- Angelika Rohde & Alexandre Tsybakov, 2010. "Estimation on High-dimensional Low Rank Matrices," Working Papers 2010-25, Centre de Recherche en Economie et Statistique.
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