Deep Bayesian Matrix Factorization

Abstract

Matrix factorization is a popular collaborative filtering technique, assuming that the matrix of ratings can be written as the inner product of two low-rank matrices, comprising latent features assigned to each user/item. Recently, several researchers have developed Bayesian treatments of matrix factorization, that infer posterior distributions over the postulated user and item latent features. As it has been shown, by allowing for taking uncertainty into account, such Bayesian inference approaches can better model sparse data, which are prevalent in real-world applications. In this paper, we consider replacing the inner product in the likelihood function of Bayesian matrix factorization with an arbitrary function that we learn from the data at the same time as we learn the latent feature posteriors; specifically, we parameterize the likelihood function using dense layer (DL) deep networks. In addition, to allow for addressing the cold-start problem, we also devise a model extension that takes into account item content, treated as side information. We provide extensive experimental evaluations on several real-world datasets; we show that our method completely outperforms state-of-the-art alternatives, without compromising computational efficiency.