  Graphical models are commonly used to represent conditional dependence
relationships between variables. There are multiple methods available for
exploring them from high-dimensional data, but almost all of them rely on the
assumption that the observations are independent and identically distributed.
At the same time, observations connected by a network are becoming increasingly
common, and tend to violate these assumptions. Here we develop a Gaussian
graphical model for observations connected by a network with potentially
different mean vectors, varying smoothly over the network. We propose an
efficient estimation algorithm and demonstrate its effectiveness on both
simulated and real data, obtaining meaningful and interpretable results on a
statistics coauthorship network. We also prove that our method estimates both
the inverse covariance matrix and the corresponding graph structure correctly
under the assumption of network âcohesionâ, which refers to the empirically
observed phenomenon of network neighbors sharing similar traits.
