Robust Bayesian Matrix Factorisation

We analyse the noise arising in collaborative filtering when formalised as a probabilistic matrix factorisation problem. We show empirically that modelling row- and column-specific variances is important, the noise being in general non-Gaussian and heteroscedastic. We also advocate for the use of a Student-t prior for the latent features as the standard Gaussian is included as a special case. We derive several variational inference algorithms and estimate the hyperparameters by type-II maximum likelihood. Experiments on real data show that the predictive performance is significantly improved.