Bayesian Graphical Regression

ABSTRACT

We consider the problem of modeling conditional independence structures in heterogenous data in the presence of additional subject-level covariates—termed graphical regression. We propose a novel specification of a conditional (in)dependence function of covariates—which allows the structure of a directed graph to vary flexibly with the covariates; imposes sparsity in both edge and covariate selection; produces both subject-specific and predictive graphs; and is computationally tractable. We provide theoretical justifications of our modeling endeavor, in terms of graphical model selection consistency. We demonstrate the performance of our method through rigorous simulation studies. We illustrate our approach in a cancer genomics-based precision medicine paradigm, where-in we explore gene regulatory networks in multiple myeloma taking prognostic clinical factors into account to obtain both population-level and subject-level gene regulatory networks. Supplementary materials for this article are available online.

Keywords:

• Directed acyclic graph
• Nonlocal prior
• Predictive network
• Subject-specific graph
• Varying graph structure

Supplementary Materials

The following eight sections comprise the online supplementary materials: A. Choice of spline bases and hyperparameters, B. Posterior Inference and prediction, C. Theoretical results, D. Additional results for simulation studies, E. Sensitivity analysis, F. Additional results for application, G. Screenshots of web application, H. Elicitation of prior ordering.

Additional information

Funding

V. Baladandayuthapani’s research was supported by grants from the National Cancer Institute (P30-CA016672, R01-CA160736, R01-CA194391, P50CA142509) and the National Science Foundation (1463233).