Escaping the curse of dimensionality in estimating multivariate transfer entropy

Jakob Runge, Jobst Heitzig, Vladimir Petoukhov, Juergen Kurths

Research output: Contribution to journalArticlepeer-review

220 Citations (Scopus)


Multivariate transfer entropy (TE) is a model-free approach to detect causalities in multivariate time series. It is able to distinguish direct from indirect causality and common drivers without assuming any underlying model. But despite these advantages it has mostly been applied in a bivariate setting as it is hard to estimate reliably in high dimensions since its definition involves infinite vectors. To overcome this limitation, we propose to embed TE into the framework of graphical models and present a formula that decomposes TE into a sum of finite-dimensional contributions that we call decomposed transfer entropy. Graphical models further provide a richer picture because they also yield the causal coupling delays. To estimate the graphical model we suggest an iterative algorithm, a modified version of the PC-algorithm with a very low estimation dimension. We present an appropriate significance test and demonstrate the method’s performance using examples of nonlinear stochastic delay-differential equations and observational climate data (sea level pressure).
Original languageEnglish
Article number258701
Number of pages5
JournalPhysical Review Letters
Issue number25
Early online date21 Jun 2012
Publication statusPublished - 22 Jun 2012


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