Abstract:
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While many statistical methods for networks involve single-network tasks (e.g., community detection), here we consider the setting where many networks are observed on a common node set. Each observation is a network, possibly weighted, with covariates at each node, and a network-level response variable. Our motivating application is neuroimaging, where edge weights might represent functional connectivity, node covariates might represent task activation at each location, and network-level response may be disease status or a score on a clinical assessment. The goal is to use the edge weights and node covariates to predict the response and identify a parsimonious and interpretable set of predictive features. We propose a method that uses a likelihood motivated by the stochastic block model, combined with penalties designed to take into account community structure (naturally occuring in neuroimaging applications) and natural groupings of edges and associated nodes. We provide a theoretical analysis and empirical results on synthetic data demonstrating good performance of the proposed method, and we apply it to data from the human connectome project.
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