Deep Poisson gamma dynamical systems
We develop deep Poisson-gamma dynamical systems (DPGDS) to model sequentially observed multivariate count data, improving previously proposed models by not only mining deep hierarchical latent structure from the data, but also capturing both first-order and long-range temporal dependencies. Using sophisticated but simple-to-implement data augmentation techniques, we derived closed-form Gibbs sampling update equations by first backward and upward propagating auxiliary latent counts, and then forward and downward sampling latent variables. Moreover, we develop stochastic gradient MCMC inference that is scalable to very long multivariate count time series. Experiments on both synthetic and a variety of real-world data demonstrate that the proposed model not only has excellent predictive performance, but also provides highly interpretable multilayer latent structure to represent hierarchical and temporal information propagation.
This paper presents Deep Poisson-Gamma Dynamical System (DPGDS) for modeling temporal multivariate count data. It is based on previously developed Gamma-Belief networks, extended to the dynamical scenarios by adding transitions of latent units in consecutive times. The paper is well written, and connections to previous papers are explained clearly.  Major comments: 1. While the temporal structure is based on transition of latent units in a Markov manner, the authors' claim about better capturing long-range temporal changes should be justified more clearly.  2. As the shape parameter in the Gamma distributions corresponding to latent units is summation of two terms, does imposing Dirichlet distributions on \Phi and \Pi makes the latent units completely identifiable?  3. I suggest to compare your performance with dynamical methods based on Gaussian Process Latent Variable Models, which are incorporated specifically to have more flexible temporal structure, if possible.  Minor comments: 1. In line 30, "separated" should be replaced by "separately". 2. The sentence starting at line 46 is better to be rewritten more clearly.