Estimating Differential Latent Variable Graphical Models with Applications to Brain Connectivity

Gaussian graphical models (Lauritzen, 1996) are used to capture complex relationships among observed variables in a variety of fields, ranging from computational biology (Friedman, 2004), genetics (Lauritzen and Sheehan, 2003), to neuroscience (Smith et al., 2011). Each node in a graphical model represents an observed variable and the (undirected) edge between two nodes is present if the nodes are conditionally dependent given all the other variables; thus (sparse) graphical models are highly interpretable and have been adopted for a wide variety of applications. Of particular interest in this manuscript are applications to cognitive neuroscience, specifically functional connectivity; the study of functional interactions between brain regions, thought to be necessary for cognition (Bullmore and Sporns, 2009). Importantly, functional connectivity is a promising biomarker for mental disorders (Castellanos et al., 2013), where the primary object of study is the differential network, that is the differences in connectivity between healthy individuals and patients. See Bielza and Larrañaga (2014) for a detailed review.