Causal Learning with the Invariance Principle

2026-05-13

AI Summary

This work addresses the ill-posed problem of causal direction identification in causal discovery by leveraging the invariance of causal mechanisms across environments within the structural causal model (SCM) framework. The authors propose a method that, under the assumption of mechanism invariance, uniquely identifies arbitrary nonlinear causal graphs and their functional mechanisms using only two auxiliary environments. This approach not only ensures identifiability of the underlying SCM but also enables valid counterfactual reasoning. Theoretical analysis and experiments on synthetic data demonstrate the method’s effectiveness, achieving accurate causal graph recovery and reliable counterfactual predictions under minimal environmental conditions.

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.

Problem

• causal discovery
• causal inference
• structural causal models
• invariance principle
• counterfactual inference

Innovation

• causal discovery
• invariance principle
• structural causal models
• nonlinear mechanisms
• counterfactual inference