# Efficient expectation propagation for posterior approximation in high-dimensional probit models

arXiv: https://arxiv.org/abs/2309.01619 · HTML: https://mlsanity.com/paper/2309.01619/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 12 references that are in the map.
- First posted on arXiv 4 Sep 2023.

## Builds on (most cited first, 9 of 9)

- [Conjugate Bayes for probit regression via unified skew-normal distributions](https://mlsanity.com/paper/1802.09565/) (2018)
- [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)
- [Bayesian conjugacy in probit, tobit, multinomial probit and extensions: A review and new results](https://mlsanity.com/paper/2206.08118/) (2022)
- [Fast and Accurate Variational Inference for Models with Many Latent Variables](https://mlsanity.com/paper/2005.07430/) (2020)
- [A closed-form filter for binary time series](https://mlsanity.com/paper/1902.06994/) (2019)
- [A Class of Conjugate Priors for Multinomial Probit Models which Includes the Multivariate Normal One](https://mlsanity.com/paper/2007.06944/) (2020)
- [Variational Inference for the Smoothing Distribution in Dynamic Probit Models](https://mlsanity.com/paper/2104.07537/) (2021)
- [Bayesian Inference for the Multinomial Probit Model under Gaussian Prior Distribution](https://mlsanity.com/paper/2206.00720/) (2022)

## Abstract (arXiv)

Bayesian binary regression is a prosperous area of research due to the computational challenges encountered by currently available methods either for high-dimensional settings or large datasets, or both. In the present work, we focus on the expectation propagation (EP) approximation of the posterior distribution in Bayesian probit regression under a multivariate Gaussian prior distribution. Adapting more general derivations in Anceschi et al. (2023), we show how to leverage results on the extended multivariate skew-normal distribution to derive an efficient implementation of the EP routine having a per-iteration cost that scales linearly in the number of covariates. This makes EP computationally feasible also in challenging high-dimensional settings, as shown in a detailed simulation study.