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

2025-02-06

AI Summary

This paper addresses the challenge of identifying indirect causal relationships in multivariate nonlinear dynamical systems. We propose MXMap, a two-stage framework that first constructs an initial causal graph using pairwise convergent cross-mapping (CCM), then refines it by extending partial cross-mapping (PCM) to a multivariate embedding formulation—termed multiPCM—to precisely prune spurious indirect edges. Our key contributions are: (i) the first formal definition of a partial causality measure under multivariate time-delay embedding, and (ii) a novel “construct–refine” paradigm for causal graph inference. Experiments on synthetic benchmarks and real-world ERA5 meteorological data demonstrate that MXMap significantly improves causal discovery accuracy, especially in high-dimensional, strongly coupled systems, while exhibiting superior robustness and interpretability compared to state-of-the-art methods.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Interdisciplinary science discovery with web data mining
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Extend PCM to multivariate for causal discovery
• Propose MXMap framework for dynamic systems
• Enhance accuracy in causal graph refinement

Innovation

• Extends PCM to multivariate embeddings
• Introduces multiPCM for indirect causality
• Proposes MXMap for causal graph refinement