  In this paper, we study the low-rank matrix completion problem, a class of
machine learning problems, that aims at the prediction of missing entries in a
partially observed matrix. Such problems appear in several challenging
applications such as collaborative filtering, image processing, and genotype
imputation. We compare the Bayesian approaches and a recently introduced
de-biased estimator which provides a useful way to build confidence intervals
of interest. From a theoretical viewpoint, the de-biased estimator comes with a
sharp minimax-optimal rate of estimation error whereas the Bayesian approach
reaches this rate with an additional logarithmic factor. Our simulation studies
show originally interesting results that the de-biased estimator is just as
good as the Bayesian estimators. Moreover, Bayesian approaches are much more
stable and can outperform the de-biased estimator in the case of small samples.
In addition, we also find that the empirical coverage rate of the confidence
intervals obtained by the de-biased estimator for an entry is absolutely lower
than of the considered credible interval. These results suggest further
theoretical studies on the estimation error and the concentration of Bayesian
methods as they are quite limited up to present.
