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.

翻译：贝叶斯二元回归是研究中的一个活跃领域，因为现有方法在处理高维设置、大规模数据集或两者兼具时面临计算挑战。本研究聚焦于多元高斯先验分布下贝叶斯probit回归后验分布的期望传播（EP）近似。通过调整Anceschi等人（2023）的更一般性推导，我们展示了如何利用扩展多元偏态正态分布的结论来推导EP算法的高效实现，该算法每次迭代的计算成本与协变量数量呈线性关系。这使得EP在具有挑战性的高维场景下也具有计算可行性，这一点通过详细的模拟研究得到了验证。