  In this paper, we propose Varying Effects Regression with Graph Estimation
(VERGE), a novel Bayesian method for feature selection in regression. Our model
has key aspects that allow it to leverage the complex structure of data sets
arising from genomics or imaging studies. We distinguish between the
predictors, which are the features utilized in the outcome prediction model,
and the subject-level covariates, which modulate the effects of the predictors
on the outcome. We construct a varying coefficients modeling framework where we
infer a network among the predictor variables and utilize this network
information to encourage the selection of related predictors. We employ
variable selection spike-and-slab priors that enable the selection of both
network-linked predictor variables and covariates that modify the predictor
effects. We demonstrate through simulation studies that our method outperforms
existing alternative methods in terms of both feature selection and predictive
accuracy. We illustrate VERGE with an application to characterizing the
influence of gut microbiome features on obesity, where we identify a set of
microbial taxa and their ecological dependence relations. We allow
subject-level covariates including sex and dietary intake variables to modify
the coefficients of the microbiome predictors, providing additional insight
into the interplay between these factors.
