On Geometry of Information Flow for Causal Inference

Area of Science:

• Interdisciplinary science
• Statistics
• Machine Learning
• Complex Systems Analysis

Background:

• Causal inference is fundamental across scientific disciplines.
• Information flow, including Granger-causality and transfer entropy, offers probabilistic methods for causal inference.
• Existing probabilistic methods like transfer entropy have boundedness limitations.

Purpose of the Study:

• To develop analysis tools for a geometric interpretation of information flow in causal inference.
• To introduce a new measure of causal inference that overcomes limitations of existing methods.
• To provide a robust framework for understanding causality in complex systems.

Main Methods:

• Geometric interpretation of information flow.
• Analysis of effective dimensionality of underlying manifolds.
• Introduction of GeoC, a causal inference measure based on fractal correlation dimension.
• Conditional application of GeoC to competing explanations of future forecasts.

Main Results:

• Demonstration of geometric interpretation of information flow.
• Development of GeoC (Geometric Causal Inference) as a new measure.
• Identification of boundedness issues with transfer entropy (Ty→x).
• GeoC shows advantages over transfer entropy in specific applications.

Conclusions:

• Geometric perspective complements probabilistic approaches to causal inference.
• GeoC offers a powerful new tool for quantifying causal relationships in complex systems.
• The developed methods are applicable to both synthetic and real-world physiological data.