# Poisson-Randomized Gamma Dynamical Systems

arXiv: https://arxiv.org/abs/1910.12991 · HTML: https://mlsanity.com/paper/1910.12991/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2019.

## Built on by (most cited first, 12 of 12)

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- [Negative-Binomial Randomized Gamma Markov Processes for Heterogeneous Overdispersed Count Time Series](https://mlsanity.com/paper/2402.18995/) (2024)
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- [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)
- [A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics](https://mlsanity.com/paper/2402.16297/) (2024)
- [Kronecker-Structured Nonparametric Spatiotemporal Point Processes](https://mlsanity.com/paper/2603.23746/) (2026)
- [Poisson-Gamma Dynamical Systems with Time-varying Transition Dynamics](https://mlsanity.com/paper/2609.00896/) (2026)

## Abstract (arXiv)

This paper presents the Poisson-randomized gamma dynamical system (PRGDS), a model for sequentially observed count tensors that encodes a strong inductive bias toward sparsity and burstiness. The PRGDS is based on a new motif in Bayesian latent variable modeling, an alternating chain of discrete Poisson and continuous gamma latent states that is analytically convenient and computationally tractable. This motif yields closed-form complete conditionals for all variables by way of the Bessel distribution and a novel discrete distribution that we call the shifted confluent hypergeometric distribution. We draw connections to closely related models and compare the PRGDS to these models in studies of real-world count data sets of text, international events, and neural spike trains. We find that a sparse variant of the PRGDS, which allows the continuous gamma latent states to take values of exactly zero, often obtains better predictive performance than other models and is uniquely capable of inferring latent structures that are highly localized in time.