Probabilistic matrix factorization (PMF) is a powerful method for modeling data associated with pairwise relationships, finding use in collaborative filtering, computational biology, and document analysis, among other areas. In many domains, there is additional information 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 multiple PMF problems via Gaussian process priors. We replace scalar latent features with functions that vary over the space of side information. The GP priors on these functions require them to vary smoothly and share information. We successfully use 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.
@conference{adams2010side,
year = {2010},
author = {Adams, Ryan P. and Dahl, George E. and Murray, Iain},
title = {Incorporating Side Information into Probabilistic Matrix Factorization Using {G}aussian Processes},
booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence (UAI)},
note = {arXiv:1003.4944 [stat.ML]},
keywords = {Gaussian processes, matrix factorization, Bayesian methods, NBA basketball, time series, UAI}
}