  A gamma process dynamic Poisson factor analysis model is proposed to
factorize a dynamic count matrix, whose columns are sequentially observed count
vectors. The model builds a novel Markov chain that sends the latent gamma
random 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. The
significant challenge of inferring the gamma shape parameters is fully
addressed, using unique data augmentation and marginalization techniques for
the negative binomial distribution. The same nonparametric Bayesian model also
applies to the factorization of a dynamic binary matrix, via a
Bernoulli-Poisson link that connects a binary observation to a latent count,
with closed-form conditional posteriors for the latent counts and efficient
computation for sparse observations. We apply the model to text and music
analysis, with state-of-the-art results.
