A Scalable Bayesian Alternative to Density Estimation with a Bilinear Softmax Function

We present a novel, scalable and Bayesian approach to modelling the occurrence of pairs (i, j) drawn from a large vocabulary. Our practical interest is in modelling (user, item) pairs in a recommender system, for which we present state of the art results on Xbox movie viewing data. The observed pairs are assumed to be generated by a simple popularity based selection process followed by censoring using a preference function. By basing inference on the well-founded principle of variational bounding, and using new site-independent bounds, we show how a scalable inference procedure can be obtained for large data sets. The model is a plausible alternative to modelling discrete densities with a bilinear softmax function.