Bayesian singular value decomposition procedure based on the horseshoe prior

Matrix completion models based on singular value decomposition have been extensively studied and discussed. Thanks to the good performance of global-local shrinkage prior, we propose in this paper a new Bayesian singular value decomposition model, where global-local horseshoe prior to the singular values, which can not only share signal information through global shrinkage parameters and local shrinkage parameters adjusted at the level of single singular values, but also achieve sparse modeling of singular values and improve accuracy of matrix completion. With the aid of mixture distribution representation for the horseshoe prior, we obtain an efficient Gibbs posterior sampling algorithm to estimate the parameters. Simulation studies and real data applications demonstrate the promising performance of the newly proposed procedure compared with existing methods.