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

Augusto Fasano; Niccolò Anceschi; Beatrice Franzolini; Giovanni Rebaudo

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arXiv · 2309.01619

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

Augusto Fasano·Niccolò Anceschi·Beatrice Franzolini·Giovanni Rebaudo

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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.

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Augusto Fasano, Niccolò Anceschi, Beatrice Franzolini, Giovanni Rebaudo. 2023-09-04. Efficient expectation propagation for posterior approximation in high-dimensional probit models. https://arxiv.org/abs/2309.01619

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