Bayesian Multi-Task Variable Selection with an Application to Differential DAG Analysis
提出一种新的变分贝叶斯算法，用于同时从多个相关数据集中选择重要变量，并扩展至有向无环图的结构学习，通过模拟和真实基因表达数据验证了效率，同时证明了后验一致性。
We study the Bayesian multi-task variable selection problem, where the goal is to select activated variables for multiple related datasets simultaneously. We propose a new variational Bayes algorithm which generalizes and improves the recently developed “sum of single effects” model of Wang et al. Motivated by differential gene network analysis in biology, we further extend our method to joint structure learning of multiple directed acyclic graphical models, a problem known to be computationally highly challenging. We propose a novel order MCMC sampler where our multi-task variable selection algorithm is used to quickly evaluate the posterior probability of each ordering. Both simulation studies and real gene expression data analysis are conducted to show the efficiency of our method. Finally, we also prove a posterior consistency result for multi-task variable selection, which provides a theoretical guarantee for the proposed algorithms. Supplementary materials for this article are available online.