Invariant Causal Prediction with Local Models

Alexander Mey, Rui M. Castro

Keywords: Causal Discovery, Invariant Causal Prediction, Structural Invariance

TL;DR: We provide a causal discovery setting with observational data based on heterogeneous data and a local linearity assumption.

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.

List Of Authors: Mey, Alexander and Castro, Rui M

Code Url: https://github.com/AlexanderMey/causal-local-linear/tree/main/UAI-code

Submission Number: 424