  Probabilistic matrix factorization (PMF) is a powerful method for modeling
data associ- ated with pairwise relationships, Finding use in collaborative
Filtering, computational bi- ology, and document analysis, among other areas.
In many domains, there are additional covariates that can assist in prediction.
For example, when modeling movie ratings, we might know when the rating
occurred, where the user lives, or what actors appear in the movie. It is
difficult, however, to incorporate this side information into the PMF model. We
propose a framework for incorporating side information by coupling together
multi- ple PMF problems via Gaussian process priors. We replace scalar latent
features with func- tions that vary over the covariate space. The GP priors on
these functions require them to vary smoothly and share information. We apply
this new method to predict the scores of professional basketball games, where
side information about the venue and date of the game are relevant for the
outcome.
