2014/08/31 by The Tien Mai, Pierre Alquier · 2 citations
Mathematics · #math.ST #stat.TH
paper · pdf · doi:10.1214/15-ejs1020
published as Electronic Journal of Statistics 9, pp. 823-841, 2015
arxiv created 2015/01/21 · arxiv updated 2015/04/08
Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of view 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.