Complete Bayesian inference of causal relationships from time series data
Marcell Stippinger1, Zsigmond Benkő1, 2, Ádám Zlatniczki1, 3, Dániel Fabó4, András Sólyom4, Loránd Erőss5, 6, András Telcs1, 3, 7, Zoltán Somogyvári1, 8
Inference of causal structure between multiple observations of a complex system gained interest in wide range of scientific disciplines, from pharmaceutics to economy, where it earned Nobel-prize for Clive Granger in 2003. We present a new analysis method called Dimensional Causality (DC), which is able to detect and distinguish all possible types of causal relations: independence, directed or circular causal connection and particularly the existence of a hidden common cause. To detect these relations between two time series, DC combines a dynamical system’s embedding-based theoretical approach with the Bayesian model inference. We believe our method is the first one able to distinguish these five causal relationships in a single framework. We validate DC on a thousand simulated instances of classical dynamical systems such as coupled Lorenz-systems and logistic maps. The performance of DC compares well with existing methods, such as Granger-causality or Sugihara’s convergent cross-mapping, even though those cannot distinguish all five relationships. We demonstrate the capabilities of our method on human neurophysiological measurements. As an example of medical application, the possible focus of epileptic seizure (an area which drives the others) is identified in a patient, based on implanted electrode recordings from the surface of the brain.