A framework for matrix factorization based on general distributions

Abstract

In this paper we extend the current state-of-the-art matrix factorization method for recommendations to general probability distributions. As shown in previous work, the standard method called Probabilistic Matrix Factorization is based on a normal distribution assumption. While there exists work in which this method is extended to other distributions, these extensions are restrictive and we experimentally show on the basis of a real data set that it is worthwhile considering more general distributions which have not been used in the literature. Our contribution lies in providing a flexible and easy-to-use framework for matrix factorization with almost no limitation on the form of the distribution used. Our approach is based on maximum likelihood estimation and a key ingredient of our proposed method is automatic differentiation. This allows for the automatic derivation of the corresponding optimization algorithm, without the need to derive it manually for each distributional assumption while simultaneously being computationally efficient. Thus, with our method it is very easy to use a wide range of even complicated distributions for any data set.