Partial cross mapping eliminates indirect causal influences

Siyang Leng, Huanfei Ma, Jürgen Kurths, Ying Cheng Lai, Wei Lin, Kazuyuki Aihara, Luonan Chen

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


Causality detection likely misidentifies indirect causations as direct ones, due to the effect of causation transitivity. Although several methods in traditional frameworks have been proposed to avoid such misinterpretations, there still is a lack of feasible methods for identifying direct causations from indirect ones in the challenging situation where the variables of the underlying dynamical system are non-separable and weakly or moderately interacting. Here, we solve this problem by developing a data-based, model-independent method of partial cross mapping based on an articulated integration of three tools from nonlinear dynamics and statistics: phase-space reconstruction, mutual cross mapping, and partial correlation. We demonstrate our method by using data from different representative models and real-world systems. As direct causations are keys to the fundamental underpinnings of a variety of complex dynamics, we anticipate our method to be indispensable in unlocking and deciphering the inner mechanisms of real systems in diverse disciplines from data.

Original languageEnglish (US)
Article number2632
JournalNature communications
Issue number1
StatePublished - Dec 1 2020

ASJC Scopus subject areas

  • Chemistry(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Physics and Astronomy(all)


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