Bayesian Adaptive Lasso with Variational Bayes for Variable Selection in High-dimensional Generalized Linear Mixed Models

TL;DR

This paper introduces a Bayesian adaptive Lasso method combined with Variational Bayes for efficient variable selection and parameter estimation in high-dimensional generalized linear mixed models, avoiding Laplace approximation.

Contribution

It presents a novel Bayesian adaptive Lasso approach with Variational Bayes for high-dimensional GLMMs, eliminating the need for Laplace approximation and enabling automatic shrinkage parameter tuning.

Findings

Effective variable selection demonstrated on simulated data

Accurate parameter estimation shown on real datasets

Implementation available in R package glmmvb

Abstract

This article describes a full Bayesian treatment for simultaneous fixed-effect selection and parameter estimation in high-dimensional generalized linear mixed models. The approach consists of using a Bayesian adaptive Lasso penalty for signal-level adaptive shrinkage and a fast Variational Bayes scheme for estimating the posterior mode of the coefficients. The proposed approach offers several advantages over the existing methods, for example, the adaptive shrinkage parameters are automatically incorporated, no Laplace approximation step is required to integrate out the random effects. The performance of our approach is illustrated on several simulated and real data examples. The algorithm is implemented in the R package glmmvb and is made available online.