Poisson random fields for dynamic feature models. (English) Zbl 1442.62070

Summary: We present the Wright-Fisher Indian buffet process (WF-IBP), a probabilistic model for time-dependent data assumed to have been generated by an unknown number of latent features. This model is suitable as a prior in Bayesian nonparametric feature allocation models in which the features underlying the observed data exhibit a dependency structure over time. More specifically, we establish a new framework for generating dependent Indian buffet processes, where the Poisson random field model from population genetics is used as a way of constructing dependent beta processes. Inference in the model is complex, and we describe a sophisticated Markov Chain Monte Carlo algorithm for exact posterior simulation. We apply our construction to develop a nonparametric focused topic model for collections of time-stamped text documents and test it on the full corpus of NIPS papers published from 1987 to 2015.


62G05 Nonparametric estimation
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62P30 Applications of statistics in engineering and industry; control charts
65C05 Monte Carlo methods
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