  In this work, we present an additive model for space-time data that splits
the data into a temporally correlated component and a spatially correlated
component. We model the spatially correlated portion using a time-varying
Gaussian graphical model. Under assumptions on the smoothness of changes in
covariance matrices, we derive strong single sample convergence results,
confirming our ability to estimate meaningful graphical structures as they
evolve over time. We apply our methodology to the discovery of time-varying
spatial structures in human brain fMRI signals.
