Nonparametric Bayesian Matrix Factorization by Power-EP

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Nan Ding, Yuan Qi, Rongjing Xiang, Ian Molloy, Ninghui Li ;
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:169-176, 2010.

Abstract

Many real-world applications can be modeled by matrix factorization. By approximating an observed data matrix as the product of two latent matrices, matrix factorization can reveal hidden structures embedded in data. A common challenge to use matrix factorization is determining the dimensionality of the latent matrices from data. Indian Buffet Processes (IBPs) enable us to apply the nonparametric Bayesian machinery to address this challenge. However, it remains a difficult task to learn nonparametric Bayesian matrix factorization models. In this paper, we propose a novel variational Bayesian method based on new equivalence classes of infinite matrices for learning these models. Furthermore, inspired by the success of nonnegative matrix factorization on many learning problems, we impose nonnegativity constraints on the latent matrices and mix variational inference with expectation propagation. This mixed inference method is unified in a power expectation propagation framework. Experimental results on image decomposition demonstrate the superior computational efficiency and the higher prediction accuracy of our methods compared to alternative Monte Carlo and variational inference methods for IBP models. We also apply the new methods to collaborative filtering and role mining and show the improved predictive performance over other matrix factorization methods.

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