A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution
|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||Online since:||2015-09-17T09:50:04Z||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||Journal:||Electronic Journal of Statistics||Volume:||9||Issue:||1||Start page:||823||End page:||841||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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