Out-of-distribution Generalization with Causal Invariant Transformations

TL;DR

This paper introduces a method for out-of-distribution generalization that leverages transformations invariant to causal features, enabling models to perform well across diverse domains without explicitly recovering causal features.

Contribution

The work proposes a novel approach using causal invariant transformations to improve OOD generalization, relaxing previous assumptions and providing theoretical guarantees.

Findings

Theoretical proof of minimax optimality with invariant transformations.

Effective regularized training procedure for OOD generalization.

Experimental validation on synthetic and real datasets showing improved performance.

Abstract

In real-world applications, it is important and desirable to learn a model that performs well on out-of-distribution (OOD) data. Recently, causality has become a powerful tool to tackle the OOD generalization problem, with the idea resting on the causal mechanism that is invariant across domains of interest. To leverage the generally unknown causal mechanism, existing works assume a linear form of causal feature or require sufficiently many and diverse training domains, which are usually restrictive in practice. In this work, we obviate these assumptions and tackle the OOD problem without explicitly recovering the causal feature. Our approach is based on transformations that modify the non-causal feature but leave the causal part unchanged, which can be either obtained from prior knowledge or learned from the training data in the multi-domain scenario. Under the setting of invariant causal mechanism, we theoretically show that if all such transformations are available, then we can learn a minimax optimal model across the domains using only single domain data. Noticing that knowing a complete set of these causal invariant transformations may be impractical, we further show that it suffices to know only a subset of these transformations. Based on the theoretical findings, a regularized training procedure is proposed to improve the OOD generalization capability. Extensive experimental results on both synthetic and real datasets verify the effectiveness of the proposed algorithm, even with only a few causal invariant transformations.