A Bayesian approach for partial Gaussian graphical models with sparsity [article]

Eunice Okome Obiang, Pascal Jézéquel, Frédéric Proïa
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
more » ... nkages 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.
doi:10.48550/arxiv.2105.10888 fatcat:fhsycbbxl5fgnktjojeaqu2vpq