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.

利用基于核函数的条件独立性测试以及基于约束的因果发现算法，本文致力于从随机动力系统中推断因果结构，证明在路径空间中，我们提出的条件独立性测试相较于现有方法表现优秀，并在允许循环的随机动力系统中，利用时间信息恢复出完整的有向图，通过实验证明我们开发的条件独立性测试结合因果发现算法在多种场景下可靠地优于基线模型。

用于随机过程的因果推断中的签名核条件独立性检验