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

TL;DR

MXMap is a new multivariate framework that improves causal discovery in dynamical systems by combining pairwise CCM tests with multivariate cross-mapping, effectively identifying direct and indirect causal relationships.

Contribution

This work extends Partial Cross Mapping to multivariate embeddings and introduces MXMap, a two-phase causal discovery framework for dynamical systems.

Findings

MXMap outperforms baseline methods in accuracy.

Effective in distinguishing direct and indirect causality.

Validated on simulated and real weather data.

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.