Causal discovery with time series data remains a challenging yet increasingly important task across many scientific domains. Convergent cross mapping (CCM) and related methods have been proposed to study time series that are generated by dynamical systems, where traditional approaches like Granger causality are unreliable. However, CCM often yields inaccurate results depending upon the quality of the data. We propose the Tangent Space Causal Inference (TSCI) method for detecting causalities in dynamical systems. TSCI works by considering vector fields as explicit representations of the systems' dynamics and checks for the degree of synchronization between the learned vector fields. The TSCI approach is model-agnostic and can be used as a drop-in replacement for CCM and its generalizations. We first present a basic version of the TSCI algorithm, which is shown to be more effective than the basic CCM algorithm with very little additional computation. We additionally present augmented versions of TSCI that leverage the expressive power of latent variable models and deep learning. We validate our theory on standard systems, and we demonstrate improved causal inference performance across a number of benchmark tasks.

翻译：时间序列数据的因果发现仍然是许多科学领域中一项具有挑战性且日益重要的任务。针对动态系统生成的时间序列，研究者提出了收敛交叉映射（CCM）及相关方法进行研究，因为传统方法（如格兰杰因果）在此类场景下并不可靠。然而，CCM的结果准确性常受数据质量影响。本文提出切空间因果推断（TSCI）方法，用于检测动态系统中的因果关系。TSCI通过将向量场视为系统动力学的显式表示，并检查学习到的向量场之间的同步程度来实现因果推断。该方法与模型无关，可作为CCM及其推广方法的直接替代方案。我们首先提出TSCI算法的基础版本，该版本在仅增加极少计算量的情况下，被证明比基础CCM算法更有效。此外，我们还提出了TSCI的增强版本，这些版本充分利用了潜变量模型和深度学习的表达能力。我们在标准系统上验证了理论，并在多个基准任务中展示了改进的因果推断性能。