Integrating Side Information in Bayesian Variable Selection via Variational Inference

Oregon Convention Center 

Bayesian variable selection (BVS) is a powerful tool in high-dimensional settings, as it incorporates prior information and facilitates model selection simultaneously. However, the potential of side information, such as previous studies or expert knowledge, to identify influential variables is often underutilized in BVS applications. For example, in a study of genetic markers of nicotine metabolite ratio p-values from previous studies are available. These p-values may be useful in determining the sparsity structure of regression coefficients, and enhance the accuracy of model results. Under the mean-field assumption, employing a spike-and-Gaussian-slab prior, variational Bayesian (VB) with the coordinate ascent variational inference (CAVI) algorithm can be used to approximate the posterior distributions. To integrate side information into variable selection, we augment our sparse linear regression model with a conditional logistic model on the impact of the side information on the variable selection indicators. In this enhanced framework, the logistic VI predominantly governs the prior inclusion probability within the spike-and-slab prior. Our simulation studies suggest that incorp

Bayesian variable selection

side information

variational inference 

Section on Bayesian Statistical Science