Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Numerical Comparisons Between Bayesian and Frequentist Low-Rank Matrix Completion: Estimation Accuracy and Uncertainty Quantification

Version 1 : Received: 21 April 2021 / Approved: 22 April 2021 / Online: 22 April 2021 (14:58:01 CEST)

How to cite: Mai, T.T. Numerical Comparisons Between Bayesian and Frequentist Low-Rank Matrix Completion: Estimation Accuracy and Uncertainty Quantification. Preprints 2021, 2021040615 (doi: 10.20944/preprints202104.0615.v1). Mai, T.T. Numerical Comparisons Between Bayesian and Frequentist Low-Rank Matrix Completion: Estimation Accuracy and Uncertainty Quantification. Preprints 2021, 2021040615 (doi: 10.20944/preprints202104.0615.v1).

Abstract

In this paper we perform numerous numerical studies for the problem of low-rank matrix completion. 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. 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.

Subject Areas

Low-rank matrix; matrix completion; Bayesian method; de-biased estimator; uncertainty quantification; confidence interval

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