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

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Granger causality (GC) analysis fails in nonlinear systems. Time-delayed mutual information (TDMI) analysis accurately identifies causal directions in nonlinear dynamical systems and neuroscience data.

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Area of Science:

  • Dynamical systems analysis
  • Causal inference methodologies
  • Neuroscience data analysis

Background:

  • Granger causality (GC) is widely used for inferring causal interactions across diverse scientific fields.
  • The validity of GC is questionable in nonlinear systems, potentially leading to inaccurate causal direction identification.
  • Nonlinearity is a common feature in many real-world dynamical systems.

Purpose of the Study:

  • To evaluate the performance of Granger causality (GC) analysis in nonlinear systems.
  • To introduce and validate time-delayed mutual information (TDMI) analysis as an alternative for nonlinear systems.
  • To compare GC and TDMI using both simulated and empirical neuroscience data.

Main Methods:

  • Construction of minimal nonlinear systems to test causality inference.
  • Application of Granger causality (GC) analysis to simulated nonlinear systems.
  • Application of time-delayed mutual information (TDMI) analysis to simulated nonlinear systems.
  • Analysis of experimental neuroscience data using both GC and TDMI methods.

Main Results:

  • Granger causality (GC) analysis demonstrated failure in inferring correct causal directions in minimal nonlinear systems, producing various incorrect outcomes.
  • Time-delayed mutual information (TDMI) analysis successfully identified the true causal interactions in these nonlinear systems.
  • In neuroscience data, TDMI analysis accurately determined interaction directions, whereas GC analysis failed to do so.

Conclusions:

  • Granger causality (GC) analysis presents significant inference hazards when applied to nonlinear dynamical systems.
  • Time-delayed mutual information (TDMI) analysis offers a robust and appropriate alternative for causal inference in the presence of system nonlinearity.
  • TDMI analysis is a valuable tool for analyzing causal interactions in complex systems, including neuronal signaling.