Invariant Causal Prediction with Local Models

TL;DR

This paper introduces L-ICP, a method for identifying causal parents of a target variable across different environments by leveraging invariance, with theoretical guarantees and experimental validation.

Contribution

It proposes a new invariant causal prediction method called L-ICP that works with local models and provides conditions for causal identifiability.

Findings

L-ICP accurately identifies causal parents in various settings.

The statistical power of L-ICP converges exponentially fast with sample size.

Experimental results demonstrate L-ICP's effectiveness in complex scenarios.

Abstract

We consider the task of identifying the causal parents of a target variable among a set of candidates from observational data. Our main assumption is that the candidate variables are observed in different environments which may, under certain assumptions, be regarded as interventions on the observed system. We assume a linear relationship between target and candidates, which can be different in each environment with the only restriction that the causal structure is invariant across environments. Within our proposed setting we provide sufficient conditions for identifiability of the causal parents and introduce a practical method called L-ICP ($\textbf{L}$ocalized $\textbf{I}$nvariant $\textbf{Ca}$usal $\textbf{P}$rediction), which is based on a hypothesis test for parent identification using a ratio of minimum and maximum statistics. We then show in a simplified setting that the statistical power of L-ICP converges exponentially fast in the sample size, and finally we analyze the behavior of L-ICP experimentally in more general settings.