Mean-field variational Bayes for sparse probit regression
针对高维二进制结果变量选择问题，提出一种均值场变分贝叶斯近似方法，在保持与MCMC相当精度的同时，计算速度快数个数量级，并给出后验包含概率和参数估计。
We consider Bayesian variable selection for binary outcomes under a probit link with a spike-and-slab prior on the regression coefficients. Motivated by the computational challenges encountered by Markov chain Monte Carlo (MCMC) samplers in high-dimensional regimes, we develop a mean-field variational Bayes approximation in which all variational factors admit closed-form updates, and the evidence lower bound is available in closed form. This, in turn, allows the development of an efficient coordinate ascent variational inference algorithm to find the optimal values of the variational parameters. The approach produces posterior inclusion probabilities and parameter estimates, enabling interpretable selection and prediction within a single framework. As shown in both simulated and real data applications, the proposed method successfully identifies the important variables and is orders of magnitude faster than MCMC, while maintaining comparable accuracy.