  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 graphical models. A third objective that is often overlooked
involves quantifying inter-subject variability and thus identifying regions or
sub-networks that demonstrate heterogeneity across subjects. Such information
is fundamental in order to thoroughly understand the human connectome. We
propose Mixed Neighborhood Selection in order 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 in order 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.
