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

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.