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Computing algebraic transfer entropy and coupling directions via transcripts.

José M Amigó1, Roberto Monetti2, Beata Graff3

  • 1Centro de Investigación Operativa, Universidad Miguel Hernández, 03202 Elche, Spain.

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Summary
This summary is machine-generated.

Algebraic transfer entropy, measuring information transfer in group-valued time series, can be linked to mutual information of transcripts. This simplifies analysis, especially for short datasets, and aids in determining coupling directions.

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Area of Science:

  • Nonlinear time series analysis
  • Information theory
  • Dynamical systems

Background:

  • Random processes in nonlinear time series analysis often have group structures (e.g., real numbers, integers).
  • Algebraic transfer entropy quantifies information transfer between coupled processes with group-valued data.
  • This measure is defined using a 'transcript' operation on pairs of group elements.

Purpose of the Study:

  • To establish a relationship between algebraic transfer entropy and mutual information of transcripts.
  • To explore the practical applications of this relationship, particularly for short time series analysis.
  • To derive conditions for determining coupling directions using these measures.

Main Methods:

  • Mathematical derivation connecting algebraic transfer entropy to mutual information of transcripts.
  • Analysis of conditions under which these measures agree on coupling direction.
  • Numerical simulations and analysis of cardiovascular data to validate findings.

Main Results:

  • Algebraic transfer entropy matches conditional mutual information of transcripts (with one less variable) under a specific constraint.
  • Weak conditions were derived for 3-dimensional algebraic transfer entropy to correctly identify coupling direction.
  • Positive results were obtained when using mutual information of transcripts for coupling direction detection in challenging cases.

Conclusions:

  • The study demonstrates a significant link between algebraic transfer entropy and mutual information of transcripts.
  • This connection offers practical advantages for analyzing complex time series data, including short datasets.
  • The findings provide a robust framework for inferring coupling directions in dynamical systems.