Conditional Local Independence Testing for Itô processes with Applications to Dynamic Causal Discovery

• URL: http://arxiv.org/abs/2506.07844v4
• Date: Wed, 08 Oct 2025 03:52:23 GMT
• Title: Conditional Local Independence Testing for Itô processes with Applications to Dynamic Causal Discovery
• Authors: Mingzhou Liu, Xinwei Sun, Yizhou Wang,
• Abstract summary: Conditional local independence describes whether one process is influenced by another given additional processes.<n>We propose a hypothesis test for conditional local independence in Ito processes.<n> Numerical verification and a real-world application to causal discovery in brain resting-state fMRIs are conducted.
• Score: 12.324391381102203
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Inferring causal relationships from dynamical systems is the central interest of many scientific inquiries. Conditional local independence, which describes whether the evolution of one process is influenced by another process given additional processes, is important for causal learning in such systems. In this paper, we propose a hypothesis test for conditional local independence in It\^o processes. Our test is grounded in the semimartingale decomposition of the It\^o process, with which we introduce a stochastic integral process that is a martingale under the null hypothesis. We then apply a test for the martingale property, quantifying potential deviation from local independence. The test statistics is estimated using the optimal filtering equation. We show the consistency of the estimation, thereby establishing the level and power of our test. Numerical verification and a real-world application to causal discovery in brain resting-state fMRIs are conducted.

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