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

Songting Li, Yanyang Xiao, Doug Zhou, David Cai

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number052216
JournalPhysical Review E
Volume97
Issue number5
DOIs
StatePublished - May 29 2018

Fingerprint

information analysis
Causal Inference
Granger Causality
nonlinear systems
Mutual Information
inference
neurology
Nonlinear Systems
finance
interactions
economy
dynamical systems
hazards
Neuroscience
nonlinearity
physics
Interaction
Social Sciences
Finance
Hazard

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Causal inference in nonlinear systems : Granger causality versus time-delayed mutual information. / Li, Songting; Xiao, Yanyang; Zhou, Doug; Cai, David.

In: Physical Review E, Vol. 97, No. 5, 052216, 29.05.2018.

Research output: Contribution to journalArticle

@article{154eb24f721c4f20af4fcd38dba362b9,
title = "Causal inference in nonlinear systems: Granger causality versus time-delayed mutual information",
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.",
author = "Songting Li and Yanyang Xiao and Doug Zhou and David Cai",
year = "2018",
month = "5",
day = "29",
doi = "10.1103/PhysRevE.97.052216",
language = "English (US)",
volume = "97",
journal = "Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics",
issn = "1063-651X",
publisher = "American Physical Society",
number = "5",

}

TY - JOUR

T1 - Causal inference in nonlinear systems

T2 - Granger causality versus time-delayed mutual information

AU - Li, Songting

AU - Xiao, Yanyang

AU - Zhou, Doug

AU - Cai, David

PY - 2018/5/29

Y1 - 2018/5/29

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85047758273&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047758273&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.97.052216

DO - 10.1103/PhysRevE.97.052216

M3 - Article

VL - 97

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 5

M1 - 052216

ER -