Abstract
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either no sparsity, sparsity, group sparsity or even sparse-group sparsity for a bi-level selection through partial correlations (direct links) between predictors and responses, thanks to spike-and-slab priors corresponding to each setting. Adaptative and global shrinkages are also incorporated in the Bayesian modeling of the direct links. An existing result for model selection consistency is reformulated to stick to our sparse and group-sparse settings, providing a theoretical guarantee under some technical assumptions. Gibbs samplers are developed and a simulation study shows the efficiency of our models which give very competitive results, especially in terms of support recovery. To conclude, a real dataset is investigated.
Funding Statement
The authors thank ALM (Angers Loire Métropole) and the ICO (Institut de Cancérologie de l’Ouest) for the financial support. This work is partially financed through the ALM grant and the “Programme opérationnel régional FEDER-FSE Pays de la Loire 2014-2020” noPL0015129 (EPICURE).
Acknowledgments
The authors warmly thank the two anonymous reviewers for their valuable suggestions and comments which clearly contributed to the improvement of the article. The authors thank Mario Campone (project leader and director of the ICO), Mathilde Colombié (scientific coordinator of EPICURE clinical trial) and Fadwa Ben Azzouz, biomathematician in Bioinfomics, for the initiation, the coordination and the smooth running of the project.
Citation
Eunice Okome Obiang. Pascal Jézéquel. Frédéric Proïa. "A Bayesian Approach for Partial Gaussian Graphical Models With Sparsity." Bayesian Anal. 18 (2) 465 - 490, June 2023. https://doi.org/10.1214/22-BA1315
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