# Negative-Binomial Randomized Gamma Markov Processes for Heterogeneous Overdispersed Count Time Series

arXiv: https://arxiv.org/abs/2402.18995 · HTML: https://mlsanity.com/paper/2402.18995/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 43 references that are in the map.
- First posted on arXiv 29 Feb 2024.

## Builds on (most cited first, 22 of 22)

- [TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics](https://mlsanity.com/paper/2002.04461/) (2020)
- [The Dynamic Embedded Topic Model](https://mlsanity.com/paper/1907.05545/) (2019)
- [Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling](https://mlsanity.com/paper/1811.12386/) (2018)
- [Inverse optimal transport](https://mlsanity.com/paper/1905.03950/) (2019)
- [Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations](https://mlsanity.com/paper/1606.01855/) (2016)
- [Infinite Edge Partition Models for Overlapping Community Detection and Link Prediction](https://mlsanity.com/paper/1501.06218/) (2015)
- [Gamma Belief Networks](https://mlsanity.com/paper/1512.03081/) (2015)
- [Deep Temporal Sigmoid Belief Networks for Sequence Modeling](https://mlsanity.com/paper/1509.07087/) (2015)
- [Poisson-Randomized Gamma Dynamical Systems](https://mlsanity.com/paper/1910.12991/) (2019)
- [Escaping the curse of dimensionality in Bayesian model based clustering](https://mlsanity.com/paper/2006.02700/) (2020)
- [The Poisson Gamma Belief Network](https://mlsanity.com/paper/1511.02199/) (2015)
- [Poisson--Gamma Dynamical Systems](https://mlsanity.com/paper/1701.05573/) (2017)
- [Deep Poisson gamma dynamical systems](https://mlsanity.com/paper/1810.11209/) (2018)
- [Nonparametric graphical model for counts](https://mlsanity.com/paper/1901.00886/) (2019)
- [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)
- [Softplus Regressions and Convex Polytopes](https://mlsanity.com/paper/1608.06383/) (2016)
- [Parsimonious Bayesian deep networks](https://mlsanity.com/paper/1805.08719/) (2018)

## Built on by (most cited first, 1 of 1)

- [Poisson-Gamma Modeling of Inter-Relational Dependencies in Dynamic Knowledge Graphs](https://mlsanity.com/paper/2607.02872/) (2026)

## Abstract (arXiv)

Modeling count-valued time series has been receiving increasing attention since count time series naturally arise in physical and social domains. Poisson gamma dynamical systems (PGDSs) are newly-developed methods, which can well capture the expressive latent transition structure and bursty dynamics behind count sequences. In particular, PGDSs demonstrate superior performance in terms of data imputation and prediction, compared with canonical linear dynamical system (LDS) based methods. Despite these advantages, PGDS cannot capture the heterogeneous overdispersed behaviours of the underlying dynamic processes. To mitigate this defect, we propose a negative-binomial-randomized gamma Markov process, which not only significantly improves the predictive performance of the proposed dynamical system, but also facilitates the fast convergence of the inference algorithm. Moreover, we develop methods to estimate both factor-structured and graph-structured transition dynamics, which enable us to infer more explainable latent structure, compared with PGDSs. Finally, we demonstrate the explainable latent structure learned by the proposed method, and show its superior performance in imputing missing data and forecasting future observations, compared with the related models.