MXMap: A Multivariate Cross Mapping Framework for Causal Discovery in Dynamical Systems

Elise Zhang, François Mirallès, Raphaël Rousseau-Rizzi, Arnaud Zinflou, Di Wu, Benoit Boulet
Proceedings of the Fourth Conference on Causal Learning and Reasoning, PMLR 275:1175-1216, 2025.

Abstract

Convergent Cross Mapping (CCM) is a powerful method for detecting causality in coupled nonlinear dynamical systems, providing a model-free approach to capture dynamic causal interactions. Partial Cross Mapping (PCM) was introduced as an extension of CCM to address indirect causality in three-variable systems by comparing cross-mapping quality between direct cause-effect mapping and indirect mapping through an intermediate conditioning variable. However, PCM remains limited to univariate delay embeddings in its cross-mapping processes. In this work, we extend PCM to the multivariate setting, introducing multiPCM, which leverages multivariate embeddings to more effectively distinguish indirect causal relationships. We further propose a multivariate cross-mapping framework (MXMap) for causal discovery in dynamical systems. This two-phase framework combines (1) pairwise CCM tests to establish an initial causal graph and (2) multiPCM to refine the graph by pruning indirect causal connections. Through experiments on simulated data and the ERA5 Reanalysis weather dataset, we demonstrate the effectiveness of MXMap. Additionally, MXMap is compared against several baseline methods, showing advantages in accuracy and causal graph refinement.

Cite this Paper

BibTeX
@InProceedings{pmlr-v275-zhang25a, title = {MXMap: A Multivariate Cross Mapping Framework for Causal Discovery in Dynamical Systems}, author = {Zhang, Elise and Mirall\`{e}s, Fran\c{c}ois and Rousseau-Rizzi, Rapha\"{e}l and Zinflou, Arnaud and Wu, Di and Boulet, Benoit}, booktitle = {Proceedings of the Fourth Conference on Causal Learning and Reasoning}, pages = {1175--1216}, year = {2025}, editor = {Huang, Biwei and Drton, Mathias}, volume = {275}, series = {Proceedings of Machine Learning Research}, month = {07--09 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v275/main/assets/zhang25a/zhang25a.pdf}, url = {https://proceedings.mlr.press/v275/zhang25a.html}, abstract = {Convergent Cross Mapping (CCM) is a powerful method for detecting causality in coupled nonlinear dynamical systems, providing a model-free approach to capture dynamic causal interactions. Partial Cross Mapping (PCM) was introduced as an extension of CCM to address indirect causality in three-variable systems by comparing cross-mapping quality between direct cause-effect mapping and indirect mapping through an intermediate conditioning variable. However, PCM remains limited to univariate delay embeddings in its cross-mapping processes. In this work, we extend PCM to the multivariate setting, introducing multiPCM, which leverages multivariate embeddings to more effectively distinguish indirect causal relationships. We further propose a multivariate cross-mapping framework (MXMap) for causal discovery in dynamical systems. This two-phase framework combines (1) pairwise CCM tests to establish an initial causal graph and (2) multiPCM to refine the graph by pruning indirect causal connections. Through experiments on simulated data and the ERA5 Reanalysis weather dataset, we demonstrate the effectiveness of MXMap. Additionally, MXMap is compared against several baseline methods, showing advantages in accuracy and causal graph refinement.} }
Endnote
%0 Conference Paper %T MXMap: A Multivariate Cross Mapping Framework for Causal Discovery in Dynamical Systems %A Elise Zhang %A François Mirallès %A Raphaël Rousseau-Rizzi %A Arnaud Zinflou %A Di Wu %A Benoit Boulet %B Proceedings of the Fourth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2025 %E Biwei Huang %E Mathias Drton %F pmlr-v275-zhang25a %I PMLR %P 1175--1216 %U https://proceedings.mlr.press/v275/zhang25a.html %V 275 %X Convergent Cross Mapping (CCM) is a powerful method for detecting causality in coupled nonlinear dynamical systems, providing a model-free approach to capture dynamic causal interactions. Partial Cross Mapping (PCM) was introduced as an extension of CCM to address indirect causality in three-variable systems by comparing cross-mapping quality between direct cause-effect mapping and indirect mapping through an intermediate conditioning variable. However, PCM remains limited to univariate delay embeddings in its cross-mapping processes. In this work, we extend PCM to the multivariate setting, introducing multiPCM, which leverages multivariate embeddings to more effectively distinguish indirect causal relationships. We further propose a multivariate cross-mapping framework (MXMap) for causal discovery in dynamical systems. This two-phase framework combines (1) pairwise CCM tests to establish an initial causal graph and (2) multiPCM to refine the graph by pruning indirect causal connections. Through experiments on simulated data and the ERA5 Reanalysis weather dataset, we demonstrate the effectiveness of MXMap. Additionally, MXMap is compared against several baseline methods, showing advantages in accuracy and causal graph refinement.
APA
Zhang, E., Mirallès, F., Rousseau-Rizzi, R., Zinflou, A., Wu, D. & Boulet, B.. (2025). MXMap: A Multivariate Cross Mapping Framework for Causal Discovery in Dynamical Systems. Proceedings of the Fourth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 275:1175-1216 Available from https://proceedings.mlr.press/v275/zhang25a.html.

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