Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data.

Area of Science:

• Statistics
• Causal Inference
• Machine Learning

Background:

• Discovering causal relationships in multivariate functional data is challenging.
• Existing methods may struggle with cyclic dependencies and interpretability.

Purpose of the Study:

• To introduce a novel functional linear structural equation model (FLSEM) for causal structure learning.
• To address cyclic graphs and enhance model interpretability through a low-dimensional embedded space.

Main Methods:

• Developed a functional linear structural equation model (FLSEM).
• Incorporated a low-dimensional causal embedded space for interpretability.
• Utilized a fully Bayesian framework for inference and uncertainty quantification.

Main Results:

• Proved causal identifiability of the proposed FLSEM under standard assumptions.
• Demonstrated superior performance in causal graph estimation compared to existing methods via simulations.
• Successfully applied the method to a real-world brain EEG dataset.

Conclusions:

• The proposed FLSEM is a powerful tool for causal discovery in multivariate functional data.
• The method offers improved interpretability and robust performance.
• Applicable to complex datasets like neuroimaging data.