Approximate Gibbs Sampler for Efficient Inference of Hierarchical Bayesian Models for Grouped Count Data

TL;DR

This paper introduces an approximate Gibbs sampler that significantly speeds up inference in hierarchical Bayesian Poisson regression models for large-scale grouped count data, maintaining accuracy.

Contribution

The paper proposes a novel approximate Gibbs sampling method that reduces computational cost for large datasets in hierarchical Bayesian models.

Findings

AGS outperforms traditional MCMC in speed for large datasets

Maintains comparable inference accuracy to exact methods

Effective on both real and synthetic data

Abstract

Hierarchical Bayesian Poisson regression models (HBPRMs) provide a flexible modeling approach of the relationship between predictors and count response variables. The applications of HBPRMs to large-scale datasets require efficient inference algorithms due to the high computational cost of inferring many model parameters based on random sampling. Although Markov Chain Monte Carlo (MCMC) algorithms have been widely used for Bayesian inference, sampling using this class of algorithms is time-consuming for applications with large-scale data and time-sensitive decision-making, partially due to the non-conjugacy of many models. To overcome this limitation, this research develops an approximate Gibbs sampler (AGS) to efficiently learn the HBPRMs while maintaining the inference accuracy. In the proposed sampler, the data likelihood is approximated with Gaussian distribution such that the conditional posterior of the coefficients has a closed-form solution. Numerical experiments using real and synthetic datasets with small and large counts demonstrate the superior performance of AGS in comparison to the state-of-the-art sampling algorithm, especially for large datasets.