Empirical Bayes Matrix Completion
This work provides a practical solution for matrix completion tasks, but it is incremental as it builds on existing singular value shrinkage methods.
The authors tackled the matrix completion problem by developing an empirical Bayes algorithm, which achieves a good trade-off between accuracy and efficiency, particularly when the difference between rows and columns is large.
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.