提出多变量因果发现框架MXMap，有效区分动态系统中直接与间接因果关系。
MXMap: A Multivariate Cross Mapping Framework for Causal Discovery in Dynamical Systems
- 引入多变量交叉映射（multiPCM），扩展传统方法处理多维数据
- 在模拟数据和气象数据上验证，准确率优于基线方法
- 适合研究复杂系统中因果结构的科研人员使用
收敛交叉映射（CCM）是一种强大的方法，用于检测耦合非线性动力系统中的因果关系，提供无需模型的动态因果交互捕捉方式。部分交叉映射（PCM）作为其扩展，通过比较直接因果映射与经中间变量传递的间接映射的交叉映射质量，解决了三变量系统中的间接因果问题。然而，PCM仍局限于单变量延迟嵌入的交叉映射过程。本文将PCM扩展至多变量设置，提出multiPCM，利用多变量嵌入更有效地区分间接因果关系。进一步提出多变量交叉映射框架（MXMap），该两阶段框架结合（1）成对CCM测试构建初始因果图，（2）通过multiPCM剔除间接因果连接以精炼图结构。在模拟数据及ERA5再分析气象数据集上的实验表明MXMap有效。与多个基线方法对比显示其在准确性和因果图精炼方面具有优势。
原文摘要 · Abstract (English)
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.
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