Causality from phases of high-dimensional nonlinear systems

Detecting causal relations in large dynamical systems is a difficult endeavor. As system dimension increases only linear approaches can be used, under the not always reasonable assumption of linear dynamics, since applications of nonlinear approaches are computationally intractable. Herein we test our recently developed information theory-based approach for causality detection from phases, appropriate for time series that exhibit well-behaved oscillatory patterns, and we expand our previous analysis to large systems with intricate connection patterns. Other than periodic-like behavior, this approach does not require any assumptions and works well for large-dimensional systems. We assess its performance on artificial data from networks of 3 or 10 coupled R & ouml;ssler oscillators and networks of 3 coupled Mackey-Glass equations. We then employ it to study the dynamics of the human brain in two test-cases, one of emotional state change in healthy subjects and one of pathological system change in epilepsy. In the course of our study, we identify some very interesting phenomena related to synchronization, which can lead any causality measure to failure. We finally discuss the steps needed to properly investigate causal relations, so that even if some real connections cannot be detected, at least false connections would not be inferred.