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.

翻译：因果发现（推断因果方向的问题）通常是不适定的。我们利用结构因果模型（SCM）的语言表明，假设因果关系是无环的，并且在多个环境中保持不变（例如，最低工资影响就业率的方式在不同地理区域是稳定的），那么仅需两个辅助环境就能推断出任意非线性机制下的因果图。此外，我们证明这意味着SCM功能机制的可识别性：作为推论，我们表明两个辅助环境足以保证正确的反事实推断。我们通过在合成数据上的实证结果支持了上述理论。