Causal Learning with the Invariance Principle

TL;DR

This paper demonstrates that using the invariance principle across two environments enables causal discovery and counterfactual inference in nonlinear SCMs, supported by empirical results.

Contribution

It shows that only two auxiliary environments are needed for causal graph identification and counterfactual inference in nonlinear models, under invariance assumptions.

Findings

Two environments suffice for causal graph identification.

Invariance leads to identifiability of SCM mechanisms.

Empirical validation on synthetic data supports theory.

Abstract

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.