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We consider the setting where many networks are observed on a common nodeset, and each observation comprises edge weights of a network, covariatesobserved at each node, and an overall response. The goal is to use the edgeweights and node covariates to predict the response while identifying aninterpretable set of predictive features. Our motivating application isneuroimaging, where edge weights encode functional connectivity measuredbetween brain regions, node covariates encode task activations at each brainregion, and the response is disease status or score on a behavioral task. Wepropose an approach that constructs feature groups based on assumed communitystructure (naturally occurring in neuroimaging applications). We propose twofeature grouping schemes that incorporate both edge weights and nodecovariates, and we derive algorithms for optimization using an overlappinggroup LASSO penalty. Empirical results on synthetic data show that our method,relative to competing approaches, has similar or improved prediction erroralong with superior support recovery, enabling a more interpretable andpotentially more accurate understanding of the underlying process. We alsoapply the method to neuroimaging data from the Human Connectome Project. Ourapproach is widely applicable in neuroimaging where interpretability is highlydesired.

Predicting Responses from Weighted Networks with Node Covariates in an Application to Neuroimaging