Approximate Bayesian inference for cumulative probit regression models

TL;DR

This paper introduces three scalable algorithms using Variational Bayes and Expectation Propagation for efficient Bayesian inference in cumulative probit models, outperforming traditional MCMC methods especially on large datasets.

Contribution

The paper presents novel scalable algorithms for Bayesian inference in cumulative probit models, improving computational efficiency and accuracy over existing MCMC methods.

Findings

Proposed algorithms are faster than MCMC for large datasets.

Algorithms demonstrate high accuracy in posterior approximation.

Case study shows practical utility in criminal network analysis.

Abstract

Ordinal categorical data are routinely encountered in many practical applications. When the primary goal is to construct a regression model for ordinal outcomes, cumulative link models represent one of the most popular choices to link the cumulative probabilities of the response with a set of covariates through a parsimonious linear predictor, shared across response categories. As the number of observations grows, standard sampling algorithms for Bayesian inference scale poorly, making posterior computation increasingly challenging for large datasets. In this article, we propose three scalable algorithms for approximating the posterior distribution of the regression coefficients in cumulative probit models relying on Variational Bayes and Expectation Propagation. We compare the proposed approaches with inference based on Markov Chain Monte Carlo, demonstrating superior computational performance and remarkable accuracy. Finally, we illustrate the utility of the proposed algorithms on a challenging case study to investigate the structure of a criminal network.