Prediction of Network Covariates Using Edge and Node Attributes

In this work 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 a network-level response. Our motivating application is neuroimaging, where edge weights could be functional connectivity measured between an atlas of brain regions, node covariates could be task activations at each brain region, and disease status or score on a behavioral task could be the response of interest. The goal is to use the edge weights and node covariates to predict the response and to identify a parsimonious and interpretable set of predictive features. We propose an approach that makes use of feature groups defined according to a community structure believed to exist in the network (naturally occurring in neuroimaging applications). We propose two schemes for forming feature groups where each group incorporates both edge weights and node covariates, and derive algorithms for both schemes optimization using an overlapping group LASSO penalty. Empirical results on synthetic data show that in certain settings our method, relative to competing approaches, has similar or improved prediction error along with superior support recovery, enabling a more interpretable and potentially a 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 human neuroimaging where interpretability and parsimony are highly desired, and can be applied in any other domain where edge and node covariates are used to predict a response.