Inferring the causal structure underlying stochastic dynamical systems from observational data holds great promise in domains ranging from science and health to finance. Such processes can often be accurately modeled via stochastic differential equations (SDEs), which naturally imply causal relationships via "which variables enter the differential of which other variables". In this paper, we develop conditional independence (CI) constraints on coordinate processes over selected intervals that are Markov with respect to the acyclic dependence graph (allowing self-loops) induced by a general SDE model. We then provide a sound and complete causal discovery algorithm, capable of handling both fully and partially observed data, and uniquely recovering the underlying or induced ancestral graph by exploiting time directionality assuming a CI oracle. Finally, to make our algorithm practically usable, we also propose a flexible, consistent signature kernel-based CI test to infer these constraints from data. We extensively benchmark the CI test in isolation and as part of our causal discovery algorithms, outperforming existing approaches in SDE models and beyond.

翻译：从观测数据推断随机动力系统背后的因果结构，在从科学、健康到金融等众多领域具有广阔前景。此类过程通常可以通过随机微分方程（SDEs）进行精确建模，这些方程通过“哪些变量进入其他变量的微分”自然地隐含了因果关系。本文针对由一般SDE模型导出的无环依赖图（允许自环）所对应的马尔可夫过程，开发了选定区间上坐标过程的条件独立性（CI）约束。随后，我们提出了一种可靠且完备的因果发现算法，该算法能够处理完全观测和部分观测数据，并在假设存在CI预言机的情况下，利用时间方向性唯一地恢复底层或诱导的祖先图。最后，为使算法具有实际可用性，我们还提出了一种灵活、一致的基于签名核的CI检验方法，用于从数据中推断这些约束。我们对该CI检验进行了广泛的基准测试，包括其独立应用以及作为我们因果发现算法的一部分，结果表明其在SDE模型及其他场景中均优于现有方法。