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Inferring causality from mapping continuity changes

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Abstract

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.

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Data Availability

The synthetic data that support the findings of this study along with the MATLAB and Python code which generate them are available from the corresponding author upon reasonable request. The real EEG data are openly available in http://archive.ics.uci.edu/ml/datasets/EEG+Database.

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Acknowledgements

We thank Xiaojun Zhao for helpful comments.

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The authors have not disclosed any funding.

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Authors and Affiliations

  1. Beijing Key Laboratory of Traffic Data Analysis and Mining, School of Computer and Information Technology, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Yifei Chen, Jing Wang & Youfang Lin

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  1. Yifei Chen
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  2. Jing Wang
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  3. Youfang Lin
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Correspondence to Jing Wang.

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Chen, Y., Wang, J. & Lin, Y. Inferring causality from mapping continuity changes. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09398-x

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