Extracting neuronal functional network dynamics via adaptive Granger causality analysis

Significance Probing functional interactions among the nodes in a network is crucial to understanding how complex systems work. Existing methodologies widely assume static network structures or Gaussian statistics or do not take account of likely sparse interactions. They are therefore not well-suited to neuronal spiking data with rapid task-dependent dynamics, binary statistics, and sparse functional dependencies. We develop an inference framework for extracting functional network dynamics from neuronal data by integrating techniques from adaptive filtering, compressed sensing, point processes, and high-dimensional statistics. We derive efficient estimation algorithms and precise statistical inference procedures. We apply our proposed techniques to experimentally recorded neuronal data to probe the neuronal functional networks underlying attentive behavior. Our techniques provide substantial gains in computation, resolution, and statistical robustness.