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Inferring causality from mapping continuity changes
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AI
DOI：10.1007/s11071-024-09398-x.png)
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Abstract
En 中文
Inferring causal relationships between time series variables unveils the interaction pattern in dynamical systems and thus contributes to our better understanding of nature's laws. An accepted notion is that measuring causality from the uncertainty reduction of the effect by considering measurements of the cause. This thought originally makes use of predictability and recently has been considered problematic when separability of subsystems does not hold. But there is no clear mathematical criterion for interpreting the specific drawbacks of this concept. In this paper, to explore the criterion, a framework similar to the accepted notion but based on mapping continuity is introduced. Under this framework, we conclude a partially testable premise that ensures the validity of inferred results. Furthermore, to put this concept into practice, a state space reconstruction technique that conforms to this framework is introduced to model unknown mappings to estimate the continuity. Finally, an approach is naturally developed to detect causality from mapping continuity changes. We validate our approach on discovering causal networks from multiple time series. In addition, we demonstrate the application in studying the effects of alcoholism on brain functional links.
Keywords:
Causal inference
Mapping continuity
Predictability
Separability
Nonlinear time series analysis