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：我们提出群组尖峰与板层变分贝叶斯（GSVB），这是一种用于群组稀疏回归的可扩展方法。针对高斯、二项和泊松等常见模型族，我们开发了快速的坐标上升变分推断（CAVI）算法。通过推导分组线性回归中变分后验的收缩率，我们为所提出的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，可作为MCMC的经济型计算替代方案，同时表现与现有MAP方法相当或更优。此外，我们分析了三个真实世界数据集，重点展示了该方法的应用价值：GSVB能够提供简约模型，兼具优异的预测性能、变量选择能力和不确定性量化功能。