Deep Poisson gamma dynamical systems
This addresses the problem of analyzing complex temporal count data for researchers in fields like neuroscience, genomics, and economics, representing an incremental improvement over existing models.
The researchers tackled modeling sequentially observed multivariate count data by developing deep Poisson-gamma dynamical systems, which demonstrated excellent predictive performance and provided highly interpretable multilayer latent structure.
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.