We introduce a class of generic spike-and-slab priors for high-dimensional linear regression with grouped variables and present a Coordinate-ascent Variational Inference (CAVI) algorithm for obtaining an optimal variational Bayes approximation. Using parameter expansion for a specific, yet comprehensive, family of slab distributions, we obtain a further gain in computational efficiency. The method can be easily extended to fitting additive models. Theoretically, we present general conditions on the generic spike-and-slab priors that enable us to derive the contraction rates for both the true posterior and the VB posterior for linear regression and additive models, of which some previous theoretical results can be viewed as special cases. Our simulation studies and real data application demonstrate that the proposed method is superior to existing methods in both variable selection and parameter estimation. Our algorithm is implemented in the R package GVSSB.

翻译：我们针对具有分组变量的高维线性回归，引入了一类通用的尖峰-板先验分布，并提出了一种坐标上升变分推断算法以获得最优的变分贝叶斯近似。通过对一类特定但全面的板分布进行参数扩展，我们进一步提升了计算效率。该方法可轻松扩展至加法模型的拟合。在理论上，我们给出了通用尖峰-板先验的通用条件，从而能够推导出线性回归和加法模型的真实后验与变分贝叶斯后验的收缩率，其中部分先前理论结果可作为特例。模拟研究和实际数据应用表明，本文所提方法在变量选择和参数估计方面均优于现有方法。该算法已实现于R包GVSSB中。