  Modeling count-valued time series has been receiving increasing attention
since count time series naturally arise in physical and social domains. Poisson
gamma dynamical systems (PGDSs) are newly-developed methods, which can well
capture the expressive latent transition structure and bursty dynamics behind
count sequences. In particular, PGDSs demonstrate superior performance in terms
of data imputation and prediction, compared with canonical linear dynamical
system (LDS) based methods. Despite these advantages, PGDS cannot capture the
heterogeneous overdispersed behaviours of the underlying dynamic processes. To
mitigate this defect, we propose a negative-binomial-randomized gamma Markov
process, which not only significantly improves the predictive performance of
the proposed dynamical system, but also facilitates the fast convergence of the
inference algorithm. Moreover, we develop methods to estimate both
factor-structured and graph-structured transition dynamics, which enable us to
infer more explainable latent structure, compared with PGDSs. Finally, we
demonstrate the explainable latent structure learned by the proposed method,
and show its superior performance in imputing missing data and forecasting
future observations, compared with the related models.
