Bayesian Multi-task Variable Selection with an Application to Differential DAG Analysis

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.