  We consider the setting where many networks are observed on a common node
set, and each observation comprises edge weights of a network, covariates
observed at each node, and an overall response. The goal is to use the edge
weights and node covariates to predict the response while identifying an
interpretable set of predictive features. Our motivating application is
neuroimaging, where edge weights encode functional connectivity measured
between brain regions, node covariates encode task activations at each brain
region, and the response is disease status or score on a behavioral task. We
propose an approach that constructs feature groups based on assumed community
structure (naturally occurring in neuroimaging applications). We propose two
feature grouping schemes that incorporate both edge weights and node
covariates, and we derive algorithms for optimization using an overlapping
group LASSO penalty. Empirical results on synthetic data show that our method,
relative to competing approaches, has similar or improved prediction error
along with superior support recovery, enabling a more interpretable and
potentially more accurate understanding of the underlying process. We also
apply the method to neuroimaging data from the Human Connectome Project. Our
approach is widely applicable in neuroimaging where interpretability is highly
desired.
