Coarsening Linear Non-Gaussian Causal Models with Cycles

TL;DR

This paper demonstrates that in linear non-Gaussian causal models with cycles, it is possible to recover a low-dimensional causal DAG from high-dimensional data, relaxing the acyclicity assumption.

Contribution

It introduces a method to identify low-dimensional causal structures in LiNG models with cycles, with polynomial time complexity and explicit sample bounds.

Findings

Low-dimensional causal DAGs can be recovered in LiNG models with cycles.

The method operates in cubic time, improving over exponential-time approaches.

Experiments validate the theoretical guarantees on synthetic data.

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.