Probabilistic Matrix Factorization with Non-random Missing Data

We propose a probabilistic matrix factorization model for collaborative filtering that learns from data that is missing not at random (MNAR). Ma-trix factorization models exhibit state-of-the-art predictive performance in collaborative filtering. However, these models usually assume that the data is missing at random (MAR), and this is rarely the case. For example, the data is not MAR if users rate items they like more than ones they dislike. When the MAR assumption is in-correct, inferences are biased and predictive per-formance can suffer. Therefore, we model both the generative process for the data and the miss-ing data mechanism. By learning these two mod-els jointly we obtain improved performance over state-of-the-art methods when predicting the rat-ings and when modeling the data observation process. We present the first viable MF model for MNAR data. Our results are promising and we expect that further research on NMAR mod-els will yield large gains in collaborative filtering. 1