Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings

•We demonstrated the success of transfer entropy in detecting information flow in two oscillators.•We explored the limitations of transfer entropy for causality inference in various scenarios.•We developed causation entropy for more reliable inference of causality in networks of coupled oscillators.

Inference of causality is central in nonlinear time series analysis and science in general. A popular approach to infer causality between two processes is to measure the information flow between them in terms of transfer entropy. Using dynamics of coupled oscillator networks, we show that although transfer entropy can successfully detect information flow in two processes, it often results in erroneous identification of network connections under the presence of indirect interactions, dominance of neighbors, or anticipatory couplings. Such effects are found to be profound for time-dependent networks. To overcome these limitations, we develop a measure called causation entropy and show that its application can lead to reliable identification of true couplings.