Inferring the structure of population-level functional connectivity networks from multi-subject functional magnetic resonance imaging data is essential for understanding the connectivity patterns underlying cognitive and behavioral functions. Graphical models provide a formal statistical framework for inferring the graph structure. However, the multi-level nature of functional magnetic resonance imaging data---where each level corresponds, for instance, to a subject---compromises the inferential validity of most existing methods. In this paper, we develop a valid inference framework for high-dimensional graphical models that accounts for cross-level heterogeneity. We introduce a neighborhood-based method to learn the graph structure and reframe the problem as that of inferring fixed effect parameters in a doubly high-dimensional linear mixed model. We then propose a LASSO-based estimator and a de-biased LASSO-based inference framework for these fixed effect parameters. We evaluate the performance of the proposed framework using benchmark simulation studies and apply it to descriptively compare graph structures between the functional connectivity networks of two predefined groups of subjects from the Human Connectome Project.

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