The paper extends causal abstraction (summarizing high-dimensional causal structure with a low-dimensional graph) to handle high-dimensional models with cycles. In the linear non-Gaussian (LiNG) setting, they show you can still recover a low-dimensional causal DAG (directed acyclic graph) even when the detailed high-dimensional model has cycles. This low-dimensional DAG is invariant across the observational equivalence class (models that differ only by cycle reversals) and can be learned in cubic time with explicit sample complexity bounds, much faster than exponential-time methods for the full equivalence class.
Main takeaways:
- Relaxes the acyclicity assumption for high-dimensional causal models while still recovering a low-dimensional acyclic summary
- The low-dimensional DAG represents the observational equivalence class of cyclic LiNG models (models differing only by cycle reversals)
- Learning algorithm runs in cubic time with provable sample complexity, far faster than exponential-time methods for the full high-dimensional equivalence class
- Provides open source code and synthetic experiments validating the theory