Continuity scaling: A rigorous framework for detecting and quantifying causality accurately

TL;DR

This paper introduces a rigorous continuity scaling framework for detecting and quantifying causality in complex nonlinear dynamical systems, outperforming existing methods by directly measuring the scaling law of system continuity.

Contribution

It develops a novel causality detection method based on continuity scaling, providing a more accurate and reliable approach aligned with natural causality interpretation.

Findings

Outperforms existing causality detection methods in accuracy

Successfully applied to both model and real-world datasets

Provides a rigorous theoretical foundation for causality measurement

Abstract

Data based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross map as conventionally implemented, we define causation through measuring the {\it scaling law} for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling based framework is rigorously established and demonstrated using datasets from model complex systems and the real world.