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

We study the Bayesian multi-task variable selection problem, where the goal is to select activated variables for multiple related data sets simultaneously. We propose a new variational Bayes algorithm which generalizes and improves the recently developed “sum of single effects” model of Wang et al. (2020a). 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.

本研究聚焦于贝叶斯多任务变量选择问题，其核心目标为同时为多个相关数据集筛选出激活变量。本文提出一种全新的变分贝叶斯（variational Bayes）算法，该算法对Wang等人（2020a）近期提出的“单效应之和”模型进行了推广与改进。受生物学中差异基因网络分析的启发，本文进一步将所提方法拓展至多有向无环图模型（directed acyclic graphical models）的联合结构学习任务——该问题被公认为计算难度极高。本文提出一种新型序贯马尔可夫链蒙特卡洛（order MCMC）采样器，利用多任务变量选择算法快速评估每种序贯的后验概率。通过仿真实验与真实基因表达数据分析，验证了本文所提方法的高效性。最后，本文还证明了多任务变量选择的后验一致性定理，为所提出的算法提供了理论保障。本文的补充材料可在线获取。