Causal Learning with the Invariance Principle
This provides a theoretical foundation for causal discovery with minimal environmental interventions, reducing the number of required environments from many to just two.
The paper shows that only two auxiliary environments are sufficient to infer causal graphs for arbitrary nonlinear mechanisms under the invariance principle, and that this also guarantees correct counterfactual inference.
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.