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

Abstract

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.

KEYWORDS:

• Joint DAG estimation
• Spike-and-slab prior
• Strong selection consistency
• SuSiE model
• Variational inference

Supplementary Materials

Appendices: Appendices.pdf gives the proof, additional simulation results and more details about the algorithm implementation.

code: Folder code includes the R code for replicating the simulation study and real data analysis presented in the article.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Acknowledgments

We thank Yuhao Wang for sharing with us the code for the joint GES method and the pre-processed real dataset.

Additional information

Funding

QZ was supported in part by NSF grant DMS-2245591.