# Poisson--Gamma Dynamical Systems

arXiv: https://arxiv.org/abs/1701.05573 · HTML: https://mlsanity.com/paper/1701.05573/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2017.

## Built on by (most cited first, 9 of 9)

- [Real-Time Variational Method for Learning Neural Trajectory and its Dynamics](https://mlsanity.com/paper/2305.11278/) (2023)
- [The Ordered Matrix Dirichlet for State-Space Models](https://mlsanity.com/paper/2212.04130/) (2022)
- [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)
- [Poisson-Gamma Modeling of Inter-Relational Dependencies in Dynamic Knowledge Graphs](https://mlsanity.com/paper/2607.02872/) (2026)
- [Recurrent Coupled Topic Modeling over Sequential Documents](https://mlsanity.com/paper/2106.13732/) (2021)
- [Spectral learning of Bernoulli linear dynamical systems models](https://mlsanity.com/paper/2303.02060/) (2023)
- [A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics](https://mlsanity.com/paper/2402.16297/) (2024)
- [Poisson-Gamma Dynamical Systems with Time-varying Transition Dynamics](https://mlsanity.com/paper/2609.00896/) (2026)

## Abstract (arXiv)

We introduce a new dynamical system for sequentially observed multivariate count data. This model is based on the gamma--Poisson construction---a natural choice for count data---and relies on a novel Bayesian nonparametric prior that ties and shrinks the model parameters, thus avoiding overfitting. We present an efficient MCMC inference algorithm that advances recent work on augmentation schemes for inference in negative binomial models. Finally, we demonstrate the model's inductive bias using a variety of real-world data sets, showing that it exhibits superior predictive performance over other models and infers highly interpretable latent structure.