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We developed transfer entropy-path weight sampling (TE-PWS), an exact computational method to quantify information flow. This new algorithm overcomes limitations of previous approximations, enabling precise analysis in complex systems.

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Area of Science:

  • Information Theory
  • Computational Neuroscience
  • Complex Systems

Background:

  • Quantifying directional information flow is crucial for understanding natural and engineered systems.
  • Transfer entropy is a key measure for information flow but often relies on uncontrolled approximations.
  • Existing methods struggle with complex models, including those with hidden variables, nonlinearity, and feedback.

Purpose of the Study:

  • Introduce a novel computational algorithm, transfer entropy-path weight sampling (TE-PWS), for exact transfer entropy quantification.
  • Enable precise measurement of information flow in diverse stochastic models.
  • Address limitations of approximate methods in complex dynamical systems.

Main Methods:

  • Developed TE-PWS, a computational algorithm leveraging polymer and path sampling techniques.
  • Computed transfer entropy as a Monte Carlo average over signal trajectory space.
  • Applied TE-PWS to linear and nonlinear systems, including those with feedback.

Main Results:

  • TE-PWS allows exact quantification of transfer entropy for any stochastic model.
  • Demonstrated that common approximate methods yield significant systematic errors and high computational costs.
  • Showcased TE-PWS's ability to handle complex scenarios like multiple hidden variables, nonlinearity, and feedback.

Conclusions:

  • TE-PWS provides an exact and efficient method for calculating transfer entropy.
  • The study highlights the inaccuracies of previously used approximate methods.
  • TE-PWS offers a powerful tool for analyzing information flow in complex systems, overcoming challenges posed by feedback loops.