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Continuity Scaling: A Rigorous Framework for Detecting and Quantifying Causality Accurately

机译:连续性缩放:用于准确检测和量化因果关系的严格框架

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摘要

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 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.
机译:在复杂的非线性动力学系统中,基于数据的检测和量化因果关系对于科学、工程和其他领域至关重要。受近年来广泛使用的方法论,即基于跨映射的技术的启发,我们开发了一个通用框架,以推进对动态因果机制的全面理解,这与因果关系的自然解释是一致的。特别是,我们不是像传统上那样测量交叉映射的平滑度,而是通过直接测量所研究的动力学系统连续性的缩放定律来定义因果关系。未发现的缩放定律能够准确、可靠和有效地检测因果关系并评估其在一般复杂动力学系统中的强度,优于现有的代表性方法。基于连续性扩展的框架是使用来自模型复杂系统和现实世界的数据集严格建立和演示的。

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