Transfer entropy for finite data

Area of Science:

• Complex systems analysis
• Information theory
• Time series analysis

Background:

• Transfer entropy quantifies directed information flow but faces challenges with continuous data.
• For discrete data, it suffers from positive bias with sparse counts and lacks statistical significance assessment.
• Existing methods struggle with finite data streams of small size or high cardinality.

Purpose of the Study:

• To develop a novel transfer entropy measure for finite discrete data streams.
• To address the limitations of existing estimators, specifically bias and lack of significance testing.
• To enable nonparametric statistical significance assessment without relying on simulations.

Main Methods:

• Derived a new transfer entropy measure by computing information content in finite data streams.
• Avoided explicit consideration of symbols as random variables.
• Ensured asymptotic equivalence to the standard plug-in estimator.

Main Results:

• The new measure is asymptotically equivalent to the standard plug-in estimator.
• It effectively remedies positive bias issues associated with sparse bin counts.
• It permits a fully nonparametric assessment of statistical significance for finite time series.
• The method is suitable for time series of small size and/or high cardinality.

Conclusions:

• The proposed transfer entropy measure offers a robust solution for analyzing information flow in discrete finite data.
• It overcomes critical limitations of traditional methods, enhancing reliability and interpretability.
• Enables rigorous statistical validation of directed information transfer in complex systems.