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ABSTRACT 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. 

In this article, we develop an analytical approach for estimating brain connectivity networks that accounts for subject heterogeneity. More specifically, we consider a novel extension of a multi‐subject Bayesian vector autoregressive model that estimates group‐specific directed brain connectivity networks and accounts for the effects of covariates on the network edges. We adopt a flexible approach, allowing for (possibly) nonlinear effects of the covariates on edge strength via a novel Bayesian nonparametric prior that employs a weighted mixture of Gaussian processes. For posterior inference, we achieve computational scalability by implementing a variational Bayes scheme. Our approach enables simultaneous estimation of group‐specific networks and selection of relevant covariate effects. We show improved performance over competing two‐stage approaches on simulated data. We apply our method on resting‐state functional magnetic resonance imaging data from children with a history of traumatic brain injury (TBI) and healthy controls to estimate the effects of age and sex on the group‐level connectivities. Our results highlight differences in the distribution of parent nodes. They also suggest alteration in the relation of age, with peak edge strength in children with TBI, and differences in effective connectivity strength between males and females.