Coarsening Linear Non-Gaussian Causal Models with Cycles

• URL: http://arxiv.org/abs/2605.10163v1
• Date: Mon, 11 May 2026 08:13:45 GMT
• Title: Coarsening Linear Non-Gaussian Causal Models with Cycles
• Abstract summary: We show that in the linear non-Gaussian setting, the high-dimensional acyclicity assumption can be relaxed.<n>We further connect identifiability of this low-dimensional DAG to existing results.<n>Our low-dimensional summary is learned in worst-case cubic time and comes with explicit bounds on the sample complexity.
• Score: 1.981773365821806
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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