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A gamma process dynamic Poisson factor analysis model is proposed tofactorize a dynamic count matrix, whose columns are sequentially observed countvectors. The model builds a novel Markov chain that sends the latent gammarandom variables at time $(t-1)$ as the shape parameters of those at time $t$,which are linked to observed or latent counts under the Poisson likelihood. Thesignificant challenge of inferring the gamma shape parameters is fullyaddressed, using unique data augmentation and marginalization techniques forthe negative binomial distribution. The same nonparametric Bayesian model alsoapplies to the factorization of a dynamic binary matrix, via aBernoulli-Poisson link that connects a binary observation to a latent count,with closed-form conditional posteriors for the latent counts and efficientcomputation for sparse observations. We apply the model to text and musicanalysis, with state-of-the-art results.

Nonparametric Bayesian Factor Analysis for Dynamic Count Matrices