Dynamic Poisson Factor Analysis

We introduce a novel dynamic model for discrete time-series data, in which the temporal sampling may be nonuniform. The model is specified by constructing a hierarchy of Poisson factor analysis blocks, one for the transitions between latent states and the other for the emissions between latent states and observations. Latent variables are binary and linked to Poisson factor analysis via Bernoulli-Poisson specifications. The model is derived for count data but can be readily modified for binary observations. We derive efficient inference via Markov chain Monte Carlo, that scales with the number of non-zeros in the data and latent binary states, yielding significant acceleration compared to related models. Experimental results on benchmark data show the proposed model achieves state-of-the-art predictive performance. Additional experiments on microbiome data demonstrate applicability of the proposed model to interesting problems in computational biology where interpretability is of utmost importance.