Latent Confounded Causal Discovery via Lie Bracket Geometry

This paper presents two novel algorithms for causal discovery in the presence of latent confounding, leveraging concepts from Kan-Do-Calculus (KDC) and information geometry. The first algorithm, BRIDGE, utilizes Radon-Nikodym derivatives to identify latent obstructions in causal vector fields, while the second, Spectral Kan-Do Flow Matching (SKFM), learns intervention fields and factors latent curvature. Both algorithms demonstrate significant efficiency improvements in discovering causal models by reducing the complexity of the search space for directed acyclic graphs (DAGs), making them valuable tools for practitioners in causal inference and machine learning.