We introduce Group Spike-and-slab Variational Bayes (GSVB), a scalable method for group sparse regression. A fast co-ordinate ascent variational inference (CAVI) algorithm is developed for several common model families including Gaussian, Binomial and Poisson. Theoretical guarantees for our proposed approach are provided by deriving contraction rates for the variational posterior in grouped linear regression. Through extensive numerical studies, we demonstrate that GSVB provides state-of-the-art performance, offering a computationally inexpensive substitute to MCMC, whilst performing comparably or better than existing MAP methods. Additionally, we analyze three real world datasets wherein we highlight the practical utility of our method, demonstrating that GSVB provides parsimonious models with excellent predictive performance, variable selection and uncertainty quantification.

翻译：本文提出组稀疏与板变分贝叶斯（GSVB），一种适用于组稀疏回归的可扩展方法。针对高斯、二项与泊松等常见模型族，我们开发了快速坐标上升变分推断（CAVI）算法。通过推导分组线性回归中变分后验的收缩率，为所提方法提供了理论保证。大量数值研究表明，GSVB实现了最先进的性能，为MCMC提供了计算成本低廉的替代方案，同时其表现与现有MAP方法相当或更优。此外，我们分析了三个真实世界数据集，突显了本方法的实用价值，证明GSVB能构建具有优异预测性能、变量选择能力和不确定性量化的简约模型。