# Deep Poisson gamma dynamical systems

arXiv: https://arxiv.org/abs/1810.11209 · HTML: https://mlsanity.com/paper/1810.11209/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2018.

## Built on by (most cited first, 8 of 8)

- [TopicNet: Semantic Graph-Guided Topic Discovery](https://mlsanity.com/paper/2110.14286/) (2021)
- [A Non-negative VAE:the Generalized Gamma Belief Network](https://mlsanity.com/paper/2408.03388/) (2024)
- [Revisiting Topic-Guided Language Models](https://mlsanity.com/paper/2312.02331/) (2023)
- [Negative-Binomial Randomized Gamma Markov Processes for Heterogeneous Overdispersed Count Time Series](https://mlsanity.com/paper/2402.18995/) (2024)
- [Sparse Data Diffusion for Scientific Simulations in Biology and Physics](https://mlsanity.com/paper/2502.02448/) (2025)
- [Curriculum Group Policy Optimization: Adaptive Sampling for Unleashing the Potential of Text-to-Image Generation](https://mlsanity.com/paper/2605.17807/) (2026)
- [Recurrent Coupled Topic Modeling over Sequential Documents](https://mlsanity.com/paper/2106.13732/) (2021)
- [A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics](https://mlsanity.com/paper/2402.16297/) (2024)

## Abstract (arXiv)

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.