Efficient expectation propagation for posterior approximation in high-dimensional probit models
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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.
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References · 9
- 2018Conjugate Bayes for probit regression via unified skew-normal distributionscited by 13
- 2019Scalable and Accurate Variational Bayes for High-Dimensional Binary Regression Modelscited by 12
- 2015Leave Pima Indians alone: binary regression as a benchmark for Bayesian computationcited by 11
- 2022Bayesian conjugacy in probit, tobit, multinomial probit and extensions: A review and new resultscited by 9
- 2020Fast and Accurate Variational Inference for Models with Many Latent Variablescited by 7
- 2019A closed-form filter for binary time seriescited by 5
- 2020A Class of Conjugate Priors for Multinomial Probit Models which Includes the Multivariate Normal Onecited by 5
- 2021Variational Inference for the Smoothing Distribution in Dynamic Probit Modelscited by 3
- 2022Bayesian Inference for the Multinomial Probit Model under Gaussian Prior Distributioncited by 1
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