Conditional Local Independence Testing for Dynamic Causal Discovery

Inferring causal relationships from dynamical systems is the central interest of many scientific inquiries. Conditional Local Independence (CLI), which describes whether the evolution of one process is influenced by another process given additional processes, is important for causal learning in such systems. However, existing CLI tests were limited to counting processes. In this paper, we propose a nonparametric CLT test for Itô processes. Specifically, we first introduce a testing statistic based on the Local Covariance Measure (LCM) by constructing a martingale from the conditional expectation of the process of interest. For estimation, we propose an efficient estimator based on the optimal filtering equation, which can achieve root-N consistency. To establish the asymptotic level and power of the test, we relax the restrictive boundedness condition to a moment bound condition, which is practical for Itô processes. We verify the proposed test in synthetic and real-world experiments.

@article{liu2025_2506.07844,
  title={ Conditional Local Independence Testing for Dynamic Causal Discovery },
  author={ Mingzhou Liu and Xinwei Sun and Yizhou Wang },
  journal={arXiv preprint arXiv:2506.07844},
  year={ 2025 }
}