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 a kernel-based test of conditional independence (CI) on "path-space" -- e.g., solutions to SDEs, but applicable beyond that -- by leveraging recent advances in signature kernels. We demonstrate strictly superior performance of our proposed CI test compared to existing approaches on path-space and provide theoretical consistency results. Then, we develop constraint-based causal discovery algorithms for acyclic stochastic dynamical systems (allowing for self-loops) that leverage temporal information to recover the entire directed acyclic graph. Assuming faithfulness and a CI oracle, we show that our algorithms are sound and complete. We empirically verify that our developed CI test in conjunction with the causal discovery algorithms outperform baselines across a range of settings.

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巨大潜力。此类过程通常可以通过随机微分方程（SDEs）精确建模，这些方程通过“哪些变量进入其他变量的微分”自然地暗示了因果关系。本文通过利用签名核的最新进展，开发了一种在“路径空间”（例如，SDEs的解，但适用范围更广）上基于核的条件独立性（CI）检验方法。我们证明了所提出的CI检验方法在路径空间上相比现有方法具有严格更优的性能，并提供了理论一致性结果。接着，我们为无环随机动力系统（允许自循环）开发了基于约束的因果发现算法，该算法利用时间信息来恢复整个有向无环图。在假设忠实性并给定一个CI预言机的条件下，我们证明了我们的算法是可靠且完备的。我们通过实验验证，我们开发的CI检验方法与因果发现算法相结合，在一系列设定中均优于基线方法。