title: A Statistical Framework to Infer Delay and Direction of Information Flow from Measurements of Complex Systems.
abstract: In neuroscience, data are typically generated from neural network activity. The resulting time series represent measurements from spatially distributed subsystems with complex interactions, weakly coupled to a high-dimensional global system. We present a statistical framework to estimate the direction of information flow and its delay in measurements from systems of this type. Informed by differential topology, gaussian process regression is employed to reconstruct measurements of putative driving systems from measurements of the driven systems. These reconstructions serve to estimate the delay of the interaction by means of an analytical criterion developed for this purpose. The model accounts for a range of possible sources of uncertainty, including temporally evolving intrinsic noise, while assuming complex nonlinear dependencies. Furthermore, we show that if information flow is delayed, this approach also allows for inference in strong coupling scenarios of systems exhibiting synchronization phenomena. The validity of the method is demonstrated with a variety of delay-coupled chaotic oscillators. In addition, we show that these results seamlessly transfer to local field potentials in cat visual cortex.
authors.affiliation: Neuroinformatics Department, Institute of Cognitive Science, University of Osnabrück, Osnabrück D-49069, Germany joschuma@uos.de.
authors.forename: Johannes
authors.initials: J
authors.lastname: Schumacher
authors.affiliation: Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, Frankfurt D-60528 Germany thomas.wunderle@esi-frankfurt.de.
authors.forename: Thomas
authors.initials: T
authors.lastname: Wunderle
authors.affiliation: Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, Frankfurt D-60528 Germany pascal.fries@esi-frankfurt.de.
authors.forename: Pascal
authors.initials: P
authors.lastname: Fries
authors.affiliation: Neuroinformatics Department, Institute of Cognitive Science, University of Osnabrück, Osnabrück D-49069, Germany fjaekel@uos.de.
authors.forename: Frank
authors.initials: F
authors.lastname: Jäkel
authors.affiliation: Neuroinformatics Department, Institute of Cognitive Science, University of Osnabrück, Osnabrück D-49069, Germany gpipa@uos.de.
authors.forename: Gordon
authors.initials: G
authors.lastname: Pipa
mesh_terms: D000465:Algorithms; D000818:Animals; D058256:Brain Waves / Q000502:physiology*; D002415:Cats; D007257:Information Theory; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D009991:Oscillometry; D013997:Time Factors; D014793:Visual Cortex / Q000166:cytology*