提出一种检验随机过程因果关系的新方法，适用于脑功能成像等动态系统。
Conditional Local Independence Testing for Itô processes with Applications to Dynamic Causal Discovery
- 基于伊藤过程的半鞅分解，构造在零假设下为鞅的随机积分过程。
- 通过检验鞅性质来量化变量间局部独立性的偏离程度，理论证明具一致性。
- 可应用于脑静息态fMRI数据的动态因果发现，实证效果良好。
从动态系统中推断因果关系是众多科学探究的核心。条件局部独立性描述了在给定其他过程的情况下，某一过程的演化是否受另一过程影响，对这类系统的因果学习至关重要。本文提出一种针对伊藤过程的条件局部独立性假设检验方法。该检验基于伊藤过程的半鞅分解，构建了一个在零假设下为鞅的随机积分过程，并应用鞅性质检验来量化偏离局部独立性的程度。检验统计量通过最优滤波方程进行估计，并证明了估计的一致性，从而确立了检验的显著性水平与功效。通过数值验证及在脑静息态fMRI数据中的实际应用，展示了方法的有效性。
原文摘要 · Abstract (English)
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 Itô processes. Our test is grounded in the semimartingale decomposition of the Itô 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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