Abstract
Matrix factorization into the product of lowrank matrices induces non-identi?ability, i.e., the mapping between the target matrix and factorized matrices is not one-to-one. In this paper, we theoretically investigate the in?uence of non-identi?ability on Bayesian matrix factorization. More speci?cally, we show that a variational Bayesian method involves regularization e?ect even when the prior is non-informative, which is intrinsically different from the maximum a posteriori approach. We also extend our analysis to empirical Bayes scenarios where hyperparameters are also learned from data.