  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.
