統計学輪講 第13回

We propose an empirical Bayes method for the Poisson matrix denoising and completion problems and develop a corresponding algorithm called EBPM. This approach is motivated by the non-central singular value shrinkage prior, which was used for the estimation of the mean matrix parameter of a matrix-variate normal distribution. Numerical experiments show that the EBPM algorithm outperforms the common nuclear norm penalized method in both matrix denoising and completion. The EBPM algorithm is hyperparameter-free and highly efficient, as opposed to the nuclear norm penalized method, in which the regularization parameter should be selected. The EBPM algorithm also performs better than the others in real-data applications.