Coarsening Linear Non-Gaussian Causal Models with Cycles

원문 초록

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 structures are acyclic. Acyclicity is helpful for causal effect identification and reasoning, but it excludes the many systems of scientific interest that contain feedback loops. We show that in the linear non-Gaussian (LiNG) setting, the acyclicity assumption on the high-dimensional structure can be relaxed while still allowing recovery of a low-dimensional causal directed acyclic graph (DAG). LiNG models with cycles are observationally identifiable only up to an equivalence class whose members differ only within their feedback loops. Our low-dimensional DAG, which is invariant across all members of this class, is therefore identifiable from observational data alone. While existing approaches for learning this equivalence class have exponential time complexity, our low-dimensional summary is learned in worst-case cubic time and comes with finite-sample guarantees. We provide open source code and experiments on synthetic data to corroborate our theoretical results.