提出可处理循环的线性非高斯因果抽象方法,高效恢复低维因果图。
Coarsening Linear Non-Gaussian Causal Models with Cycles
- 基于线性非高斯模型,放宽高维因果结构必须无环的限制。
- 低维因果图可在最坏情况立方时间学习,且有明确样本量保证。
- 适用于存在复杂循环关系的高维系统建模,如生物网络、经济系统。
因果抽象的近期研究聚焦于变量簇之间的因果结构图,旨在用低维结构总结高维因果关系。现有方法在数据学习中假设高维与低维结构均无环,虽利于因果效应识别,但排除了大量真实高维模型,限制应用范围。本文在线性非高斯(LiNG)设定下证明:高维无环假设可放松,仍能恢复低维因果有向无环图(DAG)。我们进一步将该低维DAG的可辨识性与已有结果关联:含环的LiNG模型仅在观测上可辨识至等价类,其成员通过反转有向环相互转换;而我们的低维DAG在等价类中保持不变,构成自然代表。相比现有方法对高维变量学习等价类需指数时间,本方法在最坏情况为立方时间,并提供样本复杂度显式上界。我们开源代码并在合成数据上验证理论结果。
原文摘要 · Abstract (English)
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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