An Invariant Matching Property for Distribution Generalization under Intervened Response

TL;DR

This paper introduces a new invariance principle for distribution generalization in causal models, addressing challenges when the response variable is intervened upon, and demonstrates how linear matching can enable reliable predictions across environments.

Contribution

It proposes a novel invariance property involving feature estimates for models with intervened responses, facilitating distribution generalization.

Findings

Identifies a new invariance principle for intervened responses.

Shows linear matching enables generalization across environments.

Provides simulation results validating the approach.

Abstract

The task of distribution generalization concerns making reliable prediction of a response in unseen environments. The structural causal models are shown to be useful to model distribution changes through intervention. Motivated by the fundamental invariance principle, it is often assumed that the conditional distribution of the response given its predictors remains the same across environments. However, this assumption might be violated in practical settings when the response is intervened. In this work, we investigate a class of model with an intervened response. We identify a novel form of invariance by incorporating the estimates of certain features as additional predictors. Effectively, we show this invariance is equivalent to having a deterministic linear matching that makes the generalization possible. We provide an explicit characterization of the linear matching and present our simulation results under various intervention settings.