A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution

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Title: A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution
Authors: Mai, The Tien
Alquier, Pierre
Permanent link: http://hdl.handle.net/10197/7050
Date: Apr-2015
Abstract: Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally [3, 18, 19, 24, 28]. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of view (see [7, 9, 16, 23] among others) in this problem, the theoretical optimality of Bayesian estimators have not been explored yet. In this paper, we propose a Bayesian estimator for matrix completion under general sampling distribution. We also provide an oracle inequality for this estimator. This inequality proves that, whatever the rank of the matrix to be estimated, our estimator reaches the minimax-optimal rate of convergence (up to a logarithmic factor). We end the paper with a short simulation study.
Type of material: Journal Article
Publisher: Institute of Mathematical Statistics
Keywords: Matrix completion;Bayesian analysis;PACBayesian bounds;Oracle inequality;Low-rank matrix;Gibbs sampler
DOI: 10.1214/15-EJS1020
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection
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