Efficient expectation propagation for posterior approximation in high-dimensional probit models
Abstract
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.
Cite
@article{arxiv.2309.01619,
title = {Efficient expectation propagation for posterior approximation in high-dimensional probit models},
author = {Augusto Fasano and Niccolò Anceschi and Beatrice Franzolini and Giovanni Rebaudo},
journal= {arXiv preprint arXiv:2309.01619},
year = {2023}
}