A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution
Year: 2015
Type: article
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.
Source: Electronic Journal of Statistics
DOI: 10.1214/15-ejs1020
Authors: The Tien Mai, Pierre Alquier
Institutions: Centre de Recherche en Économie et Statistique, ENSAE Paris
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $675
OpenAlex ID: W1968480431