Neuronal Functional Connectivity Graph Estimation
One of the most important scientific challenges of the twenty-first century is to understand how our brain processes information and produces behavior. As recording technologies have advanced, larger and larger numbers of neurons could be recorded simultaneously from the same brain, generating new compelling statistical problems about the identification of the structure of covariation in neural network activity. Graphical models are powerful statistical tools for the inference of neuronal functional connectivity graphs, network representations of the conditional dependence structure of the activities of hundreds to thousands of neurons. These networks let us study the functions of neuronal circuits, and the causes of their dysfunction characterizing brain disorders. However, because neuronal data are typically very noisy, special forms of statistical regularization are required to obtain meaningful representations of the functional connections of many neurons.