A causal framework for distribution generalization

TL;DR

This paper develops a causal framework for distribution generalization, analyzing how to predict responses under distribution shifts caused by interventions, and introduces a practical method for nonlinear models.

Contribution

It formalizes distribution generalization in nonlinear causal models, characterizes when causal models are minimax optimal, and proposes a consistent method called NILE for nonlinear IV settings.

Findings

NILE achieves distribution generalization in nonlinear IV models.

The framework characterizes conditions for causal models to be minimax optimal.

Empirical results demonstrate NILE's effectiveness in practice.

Abstract

We consider the problem of predicting a response $Y$ from a set of covariates $X$ when test and training distributions differ. Since such differences may have causal explanations, we consider test distributions that emerge from interventions in a structural causal model, and focus on minimizing the worst-case risk. Causal regression models, which regress the response on its direct causes, remain unchanged under arbitrary interventions on the covariates, but they are not always optimal in the above sense. For example, for linear models and bounded interventions, alternative solutions have been shown to be minimax prediction optimal. We introduce the formal framework of distribution generalization that allows us to analyze the above problem in partially observed nonlinear models for both direct interventions on $X$ and interventions that occur indirectly via exogenous variables $A$. It takes into account that, in practice, minimax solutions need to be identified from data. Our framework allows us to characterize under which class of interventions the causal function is minimax optimal. We prove sufficient conditions for distribution generalization and present corresponding impossibility results. We propose a practical method, NILE, that achieves distribution generalization in a nonlinear IV setting with linear extrapolation. We prove consistency and present empirical results.