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Bayesian Graphical Regression

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  • Yang Ni
  • Francesco C. Stingo
  • Veerabhadran Baladandayuthapani

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.

Suggested Citation

  • Yang Ni & Francesco C. Stingo & Veerabhadran Baladandayuthapani, 2019. "Bayesian Graphical Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 184-197, January.
    • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:525:p:184-197
    DOI: 10.1080/01621459.2017.1389739
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    Cited by:

    1. Yang Ni & Veerabhadran Baladandayuthapani & Marina Vannucci & Francesco C. Stingo, 2022. "Bayesian graphical models for modern biological applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 197-225, June.
    2. Yanyi Song & Xiang Zhou & Jian Kang & Max T. Aung & Min Zhang & Wei Zhao & Belinda L. Needham & Sharon L. R. Kardia & Yongmei Liu & John D. Meeker & Jennifer A. Smith & Bhramar Mukherjee, 2021. "Bayesian sparse mediation analysis with targeted penalization of natural indirect effects," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(5), pages 1391-1412, November.
    3. Calissano, Anna & Feragen, Aasa & Vantini, Simone, 2022. "Graph-valued regression: Prediction of unlabelled networks in a non-Euclidean graph space," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    4. Fangting Zhou & Kejun He & Yang Ni, 2023. "Individualized causal discovery with latent trajectory embedded Bayesian networks," Biometrics, The International Biometric Society, vol. 79(4), pages 3191-3202, December.

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