A1298
Title: Conditional local independence testing for Ito processes with applications to dynamic causal discovery
Authors: Xinwei Sun - Fudan University (China) [presenting]
Abstract: Inferring causal relationships from dynamical systems is central to 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. A hypothesis test is proposed to examine conditional local independence between stochastic random processes. The test is grounded in the semimartingale decomposition of the Ito process, with which a stochastic integral process is introduced that is a martingale under the null hypothesis. A test for the martingale property is then applied, quantifying potential deviation from local independence. The test statistic is estimated using the optimal filtering equation. Consistency of the estimation is established, thereby determining the level and power of the test. Numerical verification and a real-world application to causal discovery in brain resting-state fMRI are conducted.
