Conditional Local Independence Testing for Itô processes with Applications to Dynamic Causal Discovery
This work addresses causal discovery in dynamic systems like neuroscience, but it appears incremental as it builds on existing methods for Itô processes.
The authors tackled the problem of inferring causal relationships in dynamical systems by proposing a hypothesis test for conditional local independence in Itô processes, with results validated through numerical verification and application to brain fMRI data.
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.