# Approximate Bayesian inference for cumulative probit regression models

arXiv: https://arxiv.org/abs/2511.06967 · HTML: https://mlsanity.com/paper/2511.06967/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 47 references that are in the map.
- First posted on arXiv 10 Nov 2025.

## Builds on (most cited first, 10 of 10)

- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Expectation propagation as a way of life: A framework for Bayesian inference on partitioned data](https://mlsanity.com/paper/1412.4869/) (2014)
- [Scalable and Accurate Variational Bayes for High-Dimensional Binary Regression Models](https://mlsanity.com/paper/1911.06743/) (2019)
- [Leave Pima Indians alone: binary regression as a benchmark for Bayesian computation](https://mlsanity.com/paper/1506.08640/) (2015)
- [Partially factorized variational inference for high-dimensional mixed models](https://mlsanity.com/paper/2312.13148/) (2023)
- [Bayesian conjugacy in probit, tobit, multinomial probit and extensions: A review and new results](https://mlsanity.com/paper/2206.08118/) (2022)
- [Additive and multiplicative effects network models](https://mlsanity.com/paper/1807.08038/) (2018)
- [Extended Stochastic Block Models with Application to Criminal Networks](https://mlsanity.com/paper/2007.08569/) (2020)
- [Consistent and Scalable Composite Likelihood Estimation of Probit Models with Crossed Random Effects](https://mlsanity.com/paper/2308.15681/) (2023)
- [Scalable Expectation Propagation for Mixed-Effects Regression](https://mlsanity.com/paper/2409.14646/) (2024)

## Abstract (arXiv)

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.