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" -- solutions to SDEs -- by leveraging recent advances in signature kernels. We demonstrate strictly superior performance of our proposed CI test compared to existing approaches on path-space. Then, we develop constraint-based causal discovery algorithms for acyclic stochastic dynamical systems (allowing for loops) that leverage temporal information to recover the entire directed graph. Assuming faithfulness and a CI oracle, our algorithm is sound and complete. We empirically verify that our developed CI test in conjunction with the causal discovery algorithm reliably outperforms baselines across a range of settings.

翻译：从观测数据推断随机动力学系统的因果结构，在科学、健康及金融等领域具有重要前景。此类过程常可通过随机微分方程精确建模，其天然蕴含的因果关系体现为"哪些变量进入其他变量的微分表达式中"。本文利用签名核的最新进展，在路径空间（即随机微分方程的解空间）上开发了基于核方法的条件独立性检验。我们证明，所提出的条件独立性检验在路径空间上的性能严格优于现有方法。随后，针对无环随机动力学系统（允许存在循环结构），我们构建了基于约束的因果发现算法，通过利用时间信息恢复完整有向图。在忠实性假设与条件独立性预言机条件下，该算法具有可靠性与完备性。实验验证表明，我们开发的条件独立性检验与因果发现算法相结合，在多种场景下均能稳定超越基线方法。