Closedform Marginal Likelihood in GammaPoisson Matrix Factorization
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:15061514, 2018.
Abstract
We present novel understandings of the GammaPoisson (GaP) model, a probabilistic matrix factorization model for count data. We show that GaP can be rewritten free of the score/activation matrix. This gives us new insights about the estimation of the topic/dictionary matrix by maximum marginal likelihood estimation. In particular, this explains the robustness of this estimator to overspecified values of the factorization rank, especially its ability to automatically prune irrelevant dictionary columns, as empirically observed in previous work. The marginalization of the activation matrix leads in turn to a new Monte Carlo ExpectationMaximization algorithm with favorable properties.
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