# Poisson-Gamma Dynamical Systems with Time-varying Transition Dynamics

arXiv: https://arxiv.org/abs/2609.00896 · HTML: https://mlsanity.com/paper/2609.00896/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 1 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations](https://mlsanity.com/paper/1606.01855/) (2016)
- [Bayesian Poisson Tensor Factorization for Inferring Multilateral Relations from Sparse Dyadic Event Counts](https://mlsanity.com/paper/1506.03493/) (2015)
- [Poisson-Randomized Gamma Dynamical Systems](https://mlsanity.com/paper/1910.12991/) (2019)
- [Poisson--Gamma Dynamical Systems](https://mlsanity.com/paper/1701.05573/) (2017)
- [Scalable Generalized Dynamic Topic Models](https://mlsanity.com/paper/1803.07868/) (2018)
- [Nonparametric Bayesian Factor Analysis for Dynamic Count Matrices](https://mlsanity.com/paper/1512.08996/) (2015)
- [Nonparametric Bayesian Negative Binomial Factor Analysis](https://mlsanity.com/paper/1604.07464/) (2016)
- [A Poisson Gamma Probabilistic Model for Latent Node-group Memberships in Dynamic Networks](https://mlsanity.com/paper/1805.11054/) (2018)
- [The Hawkes Edge Partition Model for Continuous-time Event-based Temporal Networks](https://mlsanity.com/paper/2006.12952/) (2020)
- [Estimating Latent Population Flows from Aggregated Data via Inversing Multi-Marginal Optimal Transport](https://mlsanity.com/paper/2212.14527/) (2022)
- [Graph Gamma Process Generalized Linear Dynamical Systems](https://mlsanity.com/paper/2007.12852/) (2020)
- [Poisson-Gamma Modeling of Inter-Relational Dependencies in Dynamic Knowledge Graphs](https://mlsanity.com/paper/2607.02872/) (2026)

## Abstract (arXiv)

Bayesian methodologies for handling count-valued time series have gained prominence due to their ability to infer interpretable latent structures and to estimate uncertainties. Among these Bayesian models, Poisson-Gamma Dynamical Systems (PGDSs) are proven to be effective in capturing the evolving dynamics underlying observed count sequences. However, the state-of-the-art PGDS still falls short in capturing the transition dynamics that are commonly observed in real-world count time series. To mitigate this limitation, a PGDS with time-varying transition kernel (TV-PGDS), is proposed to allow the underlying transition matrices to evolve over time. Three specifically-designed Dirichlet Markov chains (Dir-Dir, Dir-Gam-Dir, PR-Gam-Dir) are constructed to accommodate heterogeneous structural mutations within these dependencies. Leveraging Dirichlet-Multinomial-Beta data augmentation techniques, a fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. Experiments show that, in comparison with related models, the proposed PGDS achieves improved predictive performance due to its capacity to learn time-varying dependency structure captured by the time-evolving transition matrices.