In this paper, we study the trade-offs of different inference approaches forBayesian matrix factorisation methods, which are commonly used for predictingmissing values, and for finding patterns in the data. In particular, weconsider Bayesian nonnegative variants of matrix factorisation andtri-factorisation, and compare non-probabilistic inference, Gibbs sampling,variational Bayesian inference, and a maximum-a-posteriori approach. Thevariational approach is new for the Bayesian nonnegative models. We comparetheir convergence, and robustness to noise and sparsity of the data, on bothsynthetic and real-world datasets. Furthermore, we extend the models with theBayesian automatic relevance determination prior, allowing the models toperform automatic model selection, and demonstrate its efficiency.
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