  We consider the probabilistic analogue to neural network matrix factorization
(Dziugaite & Roy, 2015), which we construct with Bayesian neural networks and
fit with variational inference. We find that a linear model fit with
variational inference can attain equivalent predictive performance to the
regular neural network variants on the Movielens data sets. We discuss the
implications of this result, which include some suggestions on the pros and
cons of using the neural network construction, as well as the variational
approach to inference. Such a probabilistic approach is required, however, when
considering the important class of stochastic block models. We describe a
variational inference algorithm for a neural network matrix factorization model
with nonparametric block structure and evaluate its performance on the NIPS
co-authorship data set.
