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

• URL: http://arxiv.org/abs/2309.01619v1
• Date: Mon, 4 Sep 2023 14:07:19 GMT
• Title: Efficient expectation propagation for posterior approximation in high-dimensional probit models
• Authors: Augusto Fasano, Niccol\`o Anceschi, Beatrice Franzolini, Giovanni Rebaudo
• Abstract summary: We focus on the expectation propagation (EP) approximation of the posterior distribution in Bayesian probit regression. We show how to leverage results on the extended multivariate skew-normal distribution to derive an efficient implementation of the EP routine. This makes EP computationally feasible also in challenging high-dimensional settings, as shown in a detailed simulation study.
• Score: 1.433758865948252
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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