Coarsening Linear Non-Gaussian Causal Models with Cycles
Authors: Francisco Madaleno, Francisco C Pereira, Alex Markham
Summary
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
Relevance
Not directly related to my persona/midtraining work—this is about causal structure learning and abstraction in statistical models. No obvious bridge to language model behavior, conditioning, or persona installation.
Abstract
arXiv:2605.10163v1 Announce Type: new Abstract: Recent work on causal abstraction, in particular graphical approaches focusing on causal structure between clusters of variables, aims to summarize a high-dimensional causal structure in terms of a low-dimensional one. Existing methods for learning such summaries from data assume that both the high- and low-dimensional structures are acyclic, which is helpful for causal effect identification and reasoning but excludes many high-dimensional models and thus limits applicability. We show that in the linear non-Gaussian (LiNG) setting, the high-dimensional acyclicity assumption can be relaxed while still allowing recovery of a low-dimensional causal directed acyclic graph (DAG). We further connect identifiability of this low-dimensional DAG to existing results: LiNG models with cycles are observationally identifiable only up to an equivalence class whose members differ by reversals of directed cycles; our low-dimensional DAG, which is invariant across all members of a given equivalence class, thus forms a natural representative of the class. While existing approaches for learning this observational equivalence class over high-dimensional variables have exponential time complexity, our low-dimensional summary is learned in worst-case cubic time and comes with explicit bounds on the sample complexity. We provide open source code and experiments on synthetic data to corroborate our theoretical results.