仅需两个辅助环境，就能确定非线性因果关系方向。
Causal Learning with the Invariance Principle
- 利用多环境不变性假设，通过两个额外环境推断因果图。
- 理论上证明只需两个环境即可实现因果机制可识别。
- 适合做因果推断与反事实分析的研究者参考。
因果发现——判断因果方向的问题——通常缺乏唯一解。本文基于结构因果模型（SCM）框架，假设因果关系为无环且在多个环境中保持不变（如最低工资对就业率的影响在不同地区稳定），证明：仅需两个辅助环境，即可对任意非线性机制准确推断出因果图。进一步表明，这蕴含了对SCM函数机制的可识别性：作为推论，两个辅助环境足以保证反事实推断正确。我们在合成数据上实证验证了理论结果。
原文摘要 · Abstract (English)
Causal discovery, the problem of inferring the direction of causality, is generally ill-posed. We use the language of structural causal models (SCM) to show that assuming that the causal relations are acyclic and invariant across multiple environments (e.g., the way minimum wage affects employment rate is stable across different geographical regions), \textit{only} two auxiliary environments are sufficient to infer the causal graph for arbitrary nonlinear mechanisms. Moreover, we demonstrate that this implies identifiability of the SCM functional mechanisms: as a corollary, we show that \textit{two} auxiliary environments are sufficient to guarantee correct counterfactual inference. We empirically support our theoretical results on synthetic data.
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