Embedding entropy: a nonlinear measure of dynamical causality.

Area of Science:

• Dynamical Systems
• Information Theory
• Causal Inference

Background:

• Causality research has a long history with diverse concepts and algorithms.
• Existing methods often struggle with nonlinear systems and non-separability.

Purpose of the Study:

• To present a unified mathematical framework for dynamical causality (DC).
• To introduce novel causality criteria, embedding entropy (EE) and conditional embedding entropy (cEE).
• To address limitations of existing causal inference methods, including nonlinearity and scale bias.

Main Methods:

• Developed a unified mathematical framework for dynamical causality.
• Proposed embedding entropy (EE) as a measure of DC.
• Derived conditional embedding entropy (cEE) for direct causality detection.
• Utilized numerical simulations and real-world datasets for validation.

Main Results:

• The dynamical causality framework unifies Granger causality, transfer entropy, and embedding causality.
• EE and cEE effectively measure dynamical causality and conditional causality.
• EE and cEE demonstrate advantages in solving nonlinear causal inference and non-separability problems.
• These methods reduce scale bias in numerical calculations.

Conclusions:

• Dynamical causality provides a unified perspective on time-varying causal interactions.
• Embedding entropy (EE) and conditional embedding entropy (cEE) are effective and robust tools for causal inference.
• EE and cEE offer significant improvements for analyzing complex, nonlinear systems.