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

arXiv: https://arxiv.org/abs/2203.14006 · HTML: https://mlsanity.com/paper/2203.14006/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2022.

## Built on by (most cited first, 1 of 1)

- [Detecting Causality in the Frequency Domain with Cross-Mapping Coherence](https://mlsanity.com/paper/2407.20694/) (2024)

## Abstract (arXiv)

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.