Deep Matrix Factorization for Recommender Systems with Missing Data not at Random

Abstract

Matrix Factorization is a widely used collaborative filtering method in recommender systems. However, most of them are under the assumption that the rating data is missing at random (MAR), which may not be very common. For some users, they may only rate those movies they like, so the inferences will be biased in previous models. In this paper, we proposed a deep matrix factorization method based on missing not at random (MNAR) assumption. As far as we know, this model firstly uses deep learning method to address MNAR issue. The model consists of a complete data model (CDM) and a missing data model (MDM), which are both learned by neural networks. The CDM is nonlinearly determined by two factors, the user latent features and item latent features like other matrix factorization methods. And the MDM also use these two factors but taking the rating value as extra information while training. We used variational Bayesian inference to generate the posterior distribution of our proposed model. Through extensive experiments on different kind of datasets, our proposed model produce gains in some widely used metrics, comparing with several state-of-the-art models. We also explore the performance of our model within different experimental settings.