Learning Invariant Representations under General Interventions on the Response

TL;DR

This paper introduces a new invariance principle called invariant matching property (IMP) for linear causal models, enabling better prediction across environments with interventions on responses and predictors.

Contribution

It proposes IMP, an alternative invariance capturing interventions via an additional feature, extending causal invariance principles to more general intervention scenarios.

Findings

IMP improves prediction accuracy under interventions.

Theoretical analysis of asymptotic generalization errors.

Competitive performance on real-world datasets including COVID data.

Abstract

It has become increasingly common nowadays to collect observations of feature and response pairs from different environments. As a consequence, one has to apply learned predictors to data with a different distribution due to distribution shifts. One principled approach is to adopt the structural causal models to describe training and test models, following the invariance principle which says that the conditional distribution of the response given its predictors remains the same across environments. However, this principle might be violated in practical settings when the response is intervened. A natural question is whether it is still possible to identify other forms of invariance to facilitate prediction in unseen environments. To shed light on this challenging scenario, we focus on linear structural causal models (SCMs) and introduce invariant matching property (IMP), an explicit relation to capture interventions through an additional feature, leading to an alternative form of invariance that enables a unified treatment of general interventions on the response as well as the predictors. We analyze the asymptotic generalization errors of our method under both the discrete and continuous environment settings, where the continuous case is handled by relating it to the semiparametric varying coefficient models. We present algorithms that show competitive performance compared to existing methods over various experimental settings including a COVID dataset.