Coarsening Linear Non-Gaussian Causal Models with Cycles

2026-05-11

AI Summary

This work addresses the limitation of existing causal abstraction methods, which require both high- and low-dimensional models to be acyclic and thus cannot handle high-dimensional systems containing cycles. The authors propose a novel approach that learns a low-dimensional directed acyclic graph (DAG) summary via variable clustering from a high-dimensional linear non-Gaussian cyclic causal model. This DAG remains invariant across all members of the observational equivalence class and serves as its natural representative. For the first time, the method establishes identifiability of a low-dimensional DAG while permitting cycles in the high-dimensional structure. Theoretical analysis shows the DAG can be learned in worst-case cubic time, with an explicit bound on sample complexity. Synthetic experiments validate the approach’s effectiveness, and the implementation is publicly available.

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.

Problem

• causal abstraction
• cyclic causal models
• linear non-Gaussian
• causal discovery
• dimensionality reduction

Innovation

• causal abstraction
• linear non-Gaussian models
• cyclic causal graphs
• observational equivalence class
• scalable causal discovery