# A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics

arXiv: https://arxiv.org/abs/2402.16297 · HTML: https://mlsanity.com/paper/2402.16297/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 26 Feb 2024.

## Builds on (most cited first, 13 of 13)

- [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)
- [Deep Poisson gamma dynamical systems](https://mlsanity.com/paper/1810.11209/) (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)
- [A Variational Autoencoder for Neural Temporal Point Processes with Dynamic Latent Graphs](https://mlsanity.com/paper/2312.16083/) (2023)
- [Graph Gamma Process Generalized Linear Dynamical Systems](https://mlsanity.com/paper/2007.12852/) (2020)

## Abstract (arXiv)

Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for dealing with noisy and incomplete count data. Among these 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 fails to capture the time-varying transition dynamics that are commonly observed in real-world count time sequences. To mitigate this gap, a non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time, and the evolving transition matrices are modeled by sophisticatedly-designed Dirichlet Markov chains. 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 non-stationary PGDS achieves improved predictive performance due to its capacity to learn non-stationary dependency structure captured by the time-evolving transition matrices.