B0483
Title: Time-dependent feature allocation models via Poisson Random Fields
Authors: Paul Jenkins - University of Warwick (United Kingdom) [presenting]
Valerio Perrone - University of Warwick (United Kingdom)
Dario Spano - University of Warwick (United Kingdom)
Yee Whye Teh - Oxford University (United Kingdom)
Abstract: In a feature allocation model, each data point depends on a collection of unobserved latent features. For example, we might classify a corpus of texts by describing each document via a set of topics; the topics then determine a distribution over words for that document. In a Bayesian nonparametric setting, the Indian Buffet Process (IBP) is a popular prior model in which the number of topics is unknown a priori. However, the IBP is static in that it does not account for the change in popularity of topics over time. Here we present the \emph{Poisson random field Indian Buffet Process} (PRF-IBP), a probabilistic model for collections of time-stamped documents. By adapting the Poisson random field model from population genetics, we derive a stochastic process with appealing properties including that (i) each feature popularity evolves independently as a diffusion and (ii) marginal observations at a fixed timepoint are given by the IBP. We describe a Markov Chain Monte Carlo algorithm for exact posterior simulation and illustrate our construction by analysing the topics of NIPS conference papers over 12 years. This is joint work with Valerio Perrone, Dario Spano, and Yee Whye Teh.
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