Tucker Gaussian Process for Regression and Collaborative Filtering.

We introduce the Tucker Gaussian Process (TGP), a model for regression that regularises a Gaussian Process (GP) towards simpler regression functions for enhanced generalisation performance. We derive it using a novel approach to scalable GP learning, and show that our model is particularly well-suited to grid-structured data and problems where the dependence on covariates is close to being separable. A prime example is collaborative filtering, for which our model provides an effective GP based method that has a low-rank matrix factorisation at its core. We show that TGP generalises classical Bayesian matrix factorisation models, and goes beyond them to give a natural and elegant method for incorporating side information.