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Copula Entropy Based Causal Network Discovery from Non-stationary Time Series

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Pattern Recognition (ICPR 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15307))

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Abstract

The task of deducing the causal network from time series data and identifying relationships among multiple series is increasingly vital across various sectors such as industry, medicine, and finance. Despite numerous algorithms being proposed for this purpose, the majority are predicated on the stationarity assumption. However, in disciplines like climatology and neuroscience, time series often exhibit non-stationarity, characterized by a data distribution that shifts over time. In this paper, we introduce an innovative algorithm designed to discern causal relationships from non-stationary time series. Our approach unfolds in three key steps: Initially, we harness the concept of copula entropy to estimate the conditional transfer entropy, offering a streamlined method for non-parametric conditional independence testing. Subsequently, we introduce the time index, which influences other variables at specific time lags, and by integrating the conditional transfer entropy, we execute the independence tests. This leads us to propose the CE-CDN (Copula Entropy-based Causal Discovery from Non-stationary time series), a two-stage algorithm tailored for learning the causal network and identifying change modules. Finally, through comparative analysis with existing algorithms, our experimental findings indicate that CE-CDN not only excels in managing non-stationary time series but also boasts commendable time efficiency.

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References

  1. Papana, A., Kyrtsou, C., Kugiumtzis, D., Diks, C.: Detecting causality in non-stationary time series using partial symbolic transfer entropy: evidence in financial data. Comput. Econ. 47, 341–365 (2016)

    Article  Google Scholar 

  2. Mudelsee, M.: Trend analysis of climate time series: a review of methods. Earth Sci. Rev. 190, 310–322 (2019)

    Article  Google Scholar 

  3. Cai, R., Huang, L., Chen, W., Qiao, J., Hao, Z.: Learning dynamic causal mechanisms from non-stationary data. Appl. Intell. 53, 5437–5448 (2023)

    Google Scholar 

  4. Huang, B., Zhang, K., Schölkopf, B.: Identification of Time-Dependent Causal Model: a gaussian process treatment. In: Proceedings of the 24th International Conference on Artificial Intelligence, pp. 3561–3568. AAAI (2015)

    Google Scholar 

  5. Huang, B., Zhang, K., Gong, M., Glymour, C.: Causal discovery and forecasting in nonstationary environments with state-space models. In: International Conference on Machine Learning, pp. 2901–2910. PMLR (2019)

    Google Scholar 

  6. Zhang, K., Huang, B., Zhang, J., Glymour, C., Schölkopf, B.: Causal discovery from nonstationary/heterogeneous data: skeleton estimation and orientation determination. In: International Joint Conference on Artificial Intelligence, pp. 1347–1353. IJCAI, US (2017)

    Google Scholar 

  7. Kang, M., Chen, D., Meng, N., Yan, G., Yu, W.: Identifying unique causal network from nonstationary time series. arXiv preprint arXiv:2211.10085 (2022)

  8. Ma, J., Sun, Z.: Mutual information is copula entropy. Tsinghua Sci. Technol. 16(1), 51–54 (2011)

    Article  Google Scholar 

  9. Entner, D., Hoyer, P.O.: On causal discovery from time series data using FCI. In: Proceedings of the 5th European Workshop on Probabilistic Graphical Models, pp. 121–128. PGM (2010)

    Google Scholar 

  10. Runge, J., Nowack, P., Kretschmer, M., Flaxman, S., Sejdinovic, D.: Detecting and quantifying causal associations in large nonlinear time series datasets. Sci. Adv. 5(11), eaau4996 (2019)

    Google Scholar 

  11. Hyvärinen, A., Zhang, K., Shimizu, S., Hoyer, P.O.: Estimation of a structural vector autoregression model using non-gaussianity. J. Mach. Learn. Res. 11(5), 1709–1731 (2010)

    MathSciNet  Google Scholar 

  12. Peters, J., Janzing, D., Schölkopf, B.: Causal inference on time series using restricted structural equation models. In: Proceedings of the 26th International Conference on Neural Information Processing Systems, pp. 154–162. NIPS, Curran Associates Inc., Red Hook (2013)

    Google Scholar 

  13. Pamfil, R., et al.: DYNOTEARS: structure learning from time-series data. In: International Conference on Artificial Intelligence and Statistics, pp. 1595–1605. PMLR (2020)

    Google Scholar 

  14. Sun, X., Schulte, O., Liu, G., Poupart, P.: NTS-NOTEARS: learning nonparametric DBNs with prior knowledge. arXiv preprint arXiv:2109.04286 (2021)

  15. Fujiwara, D., Koyama, K., Kiritoshi, K., Okawachi, T., Izumitani, T., Shimizu, S.: Causal discovery for non-stationary non-linear time series data using just-in-time modeling. In: Conference on Causal Learning and Reasoning, pp. 880–894. PMLR (2023)

    Google Scholar 

  16. Song, L., Kolar, M., Xing, E.: Time-varying dynamic Bayesian networks. In: Proceedings of the 22nd International Conference on Neural Information Processing Systems, pp. 1732–1740. Curran Associates Inc., Red Hook (2009)

    Google Scholar 

  17. Kraskov, A., Stögbauer, H., Grassberger, P.: Estimating mutual information. Phys. Rev. E 69(6), 066138 (2004)

    Article  MathSciNet  Google Scholar 

  18. Runge, J.: Causal network reconstruction from time series: from theoretical assumptions to practical estimation. Chaos Interdisc. J. Nonl. Sci. 28(7) (2018)

    Google Scholar 

  19. Bussmann, B., Nys, J., Latré, S.: Neural additive vector autoregression models for causal discovery in time series. In: Soares, C., Torgo, L. (eds.) DS 2021. LNCS, vol. 12986, pp. 446–460. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-88942-5_35

  20. Sugihara, G., et al.: Detecting causality in complex ecosystems. Science 338(6106), 496–500 (2012)

    Article  Google Scholar 

  21. Huang, L., He, J., Lu, C.: Review and prospect of research on the western Pacific subtropical high. J. Arid Meteorol. 30(2), 255–260 (2012)

    Google Scholar 

  22. Wang, B., Jiao, Z., Cao, J.: A study on the relationship between the sea surface temperature and the ridge of the subtropical high in the western Pacific. J. Yunnan Univ. (Nat. Sci. Edn.) 27(4), 332–336 (2005)

    Google Scholar 

  23. Tan, R., Rong, G.: Equatorial Pacific ST warming and transmission characteristics of El Nino process. J. Appl. Meteorol. Sci. 3(2), 165–172 (1992)

    Google Scholar 

  24. Zheng, J., Liu, Q.: Interactions between the tropical Pacific Ocean and the tropical Atlantic SST master modes. Oceanologia Et Limnologia Sinica 6(2), 799–806 (2010)

    Google Scholar 

  25. Zuo, J., Yu, Y., Chen, Z.: The analysis of sealevel variation factor along China coast. Adv. Earth Sci. 9(5), 48–53 (1994)

    Google Scholar 

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Authors and Affiliations

  1. The Intelligent Interconnected Systems, Hefei University of Technology, Hefei, 230009, China

    Jing Yang & Xinzhi Rao

  2. The School of Computer Science and Information Engineering, Hefei University of Technology, Hefei, 230009, China

    Jing Yang & Xinzhi Rao

Authors
  1. Jing Yang
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  2. Xinzhi Rao
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Corresponding author

Correspondence to Jing Yang .

Editor information

Editors and Affiliations

  1. University of Salford, Salford, Lancashire, UK

    Apostolos Antonacopoulos

  2. Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

    Subhasis Chaudhuri

  3. Johns Hopkins University, Baltimore, MD, USA

    Rama Chellappa

  4. Chinese Academy of Sciences, Beijing, China

    Cheng-Lin Liu

  5. IIT Kharagpur, Kharagpur, West Bengal, India

    Saumik Bhattacharya

  6. Indian Statistical Institute Kolkata, Kolkata, West Bengal, India

    Umapada Pal

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Yang, J., Rao, X. (2025). Copula Entropy Based Causal Network Discovery from Non-stationary Time Series. In: Antonacopoulos, A., Chaudhuri, S., Chellappa, R., Liu, CL., Bhattacharya, S., Pal, U. (eds) Pattern Recognition. ICPR 2024. Lecture Notes in Computer Science, vol 15307. Springer, Cham. https://doi.org/10.1007/978-3-031-78183-4_8

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  • DOI: https://doi.org/10.1007/978-3-031-78183-4_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-78182-7

  • Online ISBN: 978-3-031-78183-4

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