TY - JOUR
T1 - Causal inference in nonlinear systems
T2 - Granger causality versus time-delayed mutual information
AU - Li, Songting
AU - Xiao, Yanyang
AU - Zhou, Douglas
AU - Cai, David
N1 - Funding Information:
This work was supported by NYU Abu Dhabi Institute Grant No. G1301 (S.L., Y.X., D.Z., and D.C.), by National Science Foundation in China with Grants No. 11671259, No. 11722107, and No. 91630208, Shanghai Rising-Star Program with Grant No. 15QA1402600 (D.Z.), by National Science Foundation in China with Grant No. 31571071, NSF Grant No. DMS-1009575 (D.C.), by Shanghai Grants No. 14JC1403800, No. 15JC1400104, and the SJTU-UM Collaborative Research Program (D.C., D.Z.).
Publisher Copyright:
© 2018 American Physical Society.
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.
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U2 - 10.1103/PhysRevE.97.052216
DO - 10.1103/PhysRevE.97.052216
M3 - Article
C2 - 29906860
AN - SCOPUS:85047758273
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 -