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In this paper, we study the effects of different prior and likelihood choicesfor Bayesian matrix factorisation, focusing on small datasets. These choicescan greatly influence the predictive performance of the methods. We identifyfour groups of approaches: Gaussian-likelihood with real-valued priors,nonnegative priors, semi-nonnegative models, and finally Poisson-likelihoodapproaches. For each group we review several models from the literature,considering sixteen in total, and discuss the relations between differentpriors and matrix norms. We extensively compare these methods on eightreal-world datasets across three application areas, giving both inter- andintra-group comparisons. We measure convergence runtime speed, cross-validationperformance, sparse and noisy prediction performance, and model selectionrobustness. We offer several insights into the trade-offs between prior andlikelihood choices for Bayesian matrix factorisation on small datasets - suchas that Poisson models give poor predictions, and that nonnegative models aremore constrained than real-valued ones.

Prior and Likelihood Choices for Bayesian Matrix Factorisation on Small Datasets