Robust Bayesian Elastic Net with Spike-and-Slab Priors

Music City Center 

In high-dimensional regression problems, the demand for robust variable selection arises due to the commonly observed outliers, heavy-tailed distributions of the response variable, and model misspecifications when structured sparsity is ignored. The elastic net enjoys wide popularity in genomics studies as it can accommodate the strong correlations among omics features. Therefore, the robust elastic net in both the frequentist and Bayesian frameworks has received much attention in recent years for the robust identification of important omics features. In this study, we propose a robust Bayesian elastic net with spike-and-slab priors that overcomes the major limitations of the existing family of elastic net methods. Specifically, we have developed a fully Bayesian method that builds on the robust likelihood function to safeguard against the heterogeneity of complex diseases while accounting for structured sparsity. Incorporation of the spike-and-slab priors in the Bayesian hierarchical model has significantly improved accuracy in shrinkage estimation and variable selection. The advantages of the proposed method have been demonstrated through the simulation and real data analysis.

robust Bayesian elastic net

Markov Chain Monte Carlo

robust Bayesian variable selection

spike-and-slab priors

robust regularization

Bayesian inference analysis 

Section on Statistical Learning and Data Science