In this paper we perform a numerious numerical studies for the problem of low-rank matrix completion. We compare the Bayesain 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-optinmal 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 Bayesain estimators. Moreover, Bayesian approaches are much more stable and can outperform the de-biased estimator in the case of small samples. However, we also find that the length of the confidence intervals revealed by the de-biased estimator for an entry is absolutely shorter than the length of the considered credible interval. These suggest further theoretical studies on the estimation error and the concentration for Bayesian methods as they are being quite limited up to present.

翻译：在本文中,我们对低级别矩阵的完成问题进行了数不胜数的数字研究。 我们比较了巴伊萨因方法以及最近推出的低偏差估算器,这为建立信任度提供了有用的途径。 从理论上看, 低偏差估算器的估算率差于一个极小的迷你- optinmal 估计率差,而巴伊西亚方法则以另外的对数系数达到这一比率。 我们的模拟研究表明,最初令人感兴趣的结果是, 降低偏差估算器与巴伊萨因测量器一样好。 此外, 巴伊西亚方法比小样本的偏差估算器要稳定得多,而且比不偏差的估算器要好得多。 然而,我们也发现, 偏差估算器对某一条目显示的信任度间隔的长度绝对短于被认为是可信的间隔的长度。 这表明,关于估计误差和巴伊西亚方法的集中度的进一步理论研究与目前相比相当有限。