Incorporating Side Information in Probabilistic Matrix Factorization with Gaussian Processes

Ryan Adams, George Dahl, Iain Murray
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:1-9, 2010.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-adams10a, title = {Incorporating Side Information in Probabilistic Matrix Factorization with {G}aussian Processes}, author = {Adams, Ryan and Dahl, George and Murray, Iain}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {1--9}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/adams10a/adams10a.pdf}, url = {https://proceedings.mlr.press/r8/adams10a.html}, abstract = {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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Incorporating Side Information in Probabilistic Matrix Factorization with Gaussian Processes %A Ryan Adams %A George Dahl %A Iain Murray %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-adams10a %I PMLR %P 1--9 %U https://proceedings.mlr.press/r8/adams10a.html %V R8 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
Adams, R., Dahl, G. & Murray, I.. (2010). Incorporating Side Information in Probabilistic Matrix Factorization with Gaussian Processes. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:1-9 Available from https://proceedings.mlr.press/r8/adams10a.html. Reissued by PMLR on 04 October 2026.

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