Causal inference in nonlinear systems: Granger causality versus time-delayed mutual information

Songting Li, Yanyang Xiao, Douglas Zhou, and David Cai
Phys. Rev. E 97, 052216 – Published 29 May 2018

Abstract

The Granger causality (GC) analysis has been extensively applied to infer causal interactions in dynamical systems arising from economy and finance, physics, bioinformatics, neuroscience, social science, and many other fields. In the presence of potential nonlinearity in these systems, the validity of the GC analysis in general is questionable. To illustrate this, here we first construct minimal nonlinear systems and show that the GC analysis fails to infer causal relations in these systems—it gives rise to all types of incorrect causal directions. In contrast, we show that the time-delayed mutual information (TDMI) analysis is able to successfully identify the direction of interactions underlying these nonlinear systems. We then apply both methods to neuroscience data collected from experiments and demonstrate that the TDMI analysis but not the GC analysis can identify the direction of interactions among neuronal signals. Our work exemplifies inference hazards in the GC analysis in nonlinear systems and suggests that the TDMI analysis can be an appropriate tool in such a case.

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  • Received 16 January 2018

DOI:https://doi.org/10.1103/PhysRevE.97.052216

©2018 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsGeneral Physics

Authors & Affiliations

Songting Li

  • Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA

Yanyang Xiao

  • Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA and NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates

Douglas Zhou*

  • School of Mathematical Sciences, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China

David Cai

  • Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA; NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates; and School of Mathematical Sciences, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China

  • *zdz@sjtu.edu.cn
  • Dedicated to David Cai.

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Issue

Vol. 97, Iss. 5 — May 2018

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