In this paper, we study the Bayesian multi-task variable selection problem, where the goal is to select activated variables for multiple related data sets simultaneously. Our proposed method generalizes the spike-and-slab prior to multiple data sets, and we prove its posterior consistency in high-dimensional regimes. To calculate the posterior distribution, we propose a novel variational Bayes algorithm based on the recently developed "sum of single effects" model of Wang et al. (2020). Finally, motivated by differential gene network analysis in biology, we extend our method to joint learning of multiple directed acyclic graphical models. Both simulation studies and real gene expression data analysis are conducted to show the effectiveness of the proposed method.

翻译：在本文中,我们研究了巴伊西亚多任务变量选择问题, 目标是同时选择多个相关数据集的活变数。 我们建议的方法概括了多个数据集之前的钉和板。 我们证明了其在高维系统中的后台一致性。 为了计算后台分布, 我们根据Wang等人( 202020年)最近开发的“ 单一效果总和” 模型, 提出了一个新的变异贝亚算法。 最后, 在生物学中不同基因网络分析的推动下, 我们把方法推广到共同学习多方向的环球图形模型。 进行模拟研究和真实基因表达数据分析是为了显示拟议方法的有效性 。