Poisson--Gamma Dynamical Systems

TL;DR

This paper introduces a novel Bayesian nonparametric dynamical system for multivariate count data, leveraging gamma--Poisson construction and an efficient inference algorithm, demonstrating superior predictive performance and interpretability.

Contribution

The paper presents a new gamma--Poisson based dynamical model with a novel prior and an efficient MCMC inference method for multivariate count data.

Findings

Superior predictive performance over existing models

Infers highly interpretable latent structures

Effective on various real-world datasets

Abstract

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.