  We tackle the problem of collaborative filtering (CF) with side information,
through the lens of Gaussian Process (GP) regression. Driven by the idea of
using the kernel to explicitly model user-item similarities, we formulate the
GP in a way that allows the incorporation of low-rank matrix factorisation,
arriving at our model, the Tucker Gaussian Process (TGP). Consequently, TGP
generalises classical Bayesian matrix factorisation models, and goes beyond
them to give a natural and elegant method for incorporating side information,
giving enhanced predictive performance for CF problems. Moreover we show that
it is a novel model for regression, especially well-suited to grid-structured
data and problems where the dependence on covariates is close to being
separable.
