In neuroimaging data analysis, Gaussian graphical models are often used to model statistical dependencies across spatially remote brain regions known as functional connectivity. Typically, data is collected across a cohort of subjects and the scientific objectives consist of estimating population and subject-specific connectivity networks. A third objective that is often overlooked involves quantifying inter-subject variability, and thus identifying regions or subnetworks that demonstrate heterogeneity across subjects. Such information is crucial to thoroughly understand the human connectome. We propose Mixed Neighborhood Selection to simultaneously address the three aforementioned objectives. By recasting covariance selection as a neighborhood selection problem, we are able to efficiently learn the topology of each node. We introduce an additional mixed effect component to neighborhood selection to simultaneously estimate a graphical model for the population of subjects as well as for each individual subject. The proposed method is validated empirically through a series of simulations and applied to resting state data for healthy subjects taken from the ABIDE consortium.
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