Distributed, partially collapsed MCMC for Bayesian Nonparametrics
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Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:36853695, 2020.
Abstract
Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonlyused models like the Dirichlet process and the betaBernoulli process can be expressed using, are decomposable into independent submeasures. We use this decomposition to partition the latent measure into a finite measure containing only instantiated components, and an infinite measure containing all other components. We then select different inference algorithms for the two components: uncollapsed samplers mix well on the finite measure, while collapsed samplers mix well on the infinite, sparsely occupied tail. The resulting hybrid algorithm can be applied to a wide class of models, and can be easily distributed to allow scalable inference without sacrificing asymptotic convergence guarantees.
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