# Empirical Bayes Matrix Completion

## TL;DR

This paper introduces an empirical Bayes algorithm for matrix completion that leverages singular value shrinkage, offering a parameter-tuning free, efficient, and accurate solution especially effective for matrices with large row-column disparities.

## Contribution

The paper presents a novel EB algorithm for matrix completion based on singular value shrinkage, eliminating heuristic tuning and improving performance over existing methods.

## Key findings

- Achieves a good balance between accuracy and efficiency.
- Performs well when the number of rows and columns differ greatly.
- Demonstrates practical utility on real datasets.

## Abstract

We develop an empirical Bayes (EB) algorithm for the matrix completion problems. The EB algorithm is motivated from the singular value shrinkage estimator for matrix means by Efron and Morris (1972). Since the EB algorithm is essentially the EM algorithm applied to a simple model, it does not require heuristic parameter tuning other than tolerance. Numerical results demonstrated that the EB algorithm achieves a good trade-off between accuracy and efficiency compared to existing algorithms and that it works particularly well when the difference between the number of rows and columns is large. Application to real data also shows the practical utility of the EB algorithm.