Coarsening Linear Non-Gaussian Causal Models with Cycles
2026-05-11 • Artificial Intelligence
Artificial IntelligenceMachine Learning
AI summaryⓘ
The authors study how to simplify complex cause-and-effect relationships by summarizing them into fewer key parts. Traditional methods assume no feedback loops in both detailed and summary models, limiting their use. They show that in a specific model type (linear non-Gaussian), the detailed model can have cycles, but the simplified summary still forms a clear cause-effect diagram without cycles. Their summary captures essential causal information shared by all similar models and can be computed efficiently with proven guarantees. They support their findings with experiments and provide code for others to use.
causal abstractiondirected acyclic graph (DAG)linear non-Gaussian model (LiNG)causal structurecycles in graphsobservational equivalencecausal effect identificationsample complexitygraphical models
Authors
Francisco Madaleno, Francisco C Pereira, Alex Markham
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.