To avoid failures on out-of-distribution data, recent works have sought to extract features that have a stable or invariant relationship with the label across domains, discarding the "spurious" or unstable features whose relationship with the label changes across domains. However, unstable features often carry complementary information about the label that could boost performance if used correctly in the test domain. Our main contribution is to show that it is possible to learn how to use these unstable features in the test domain without labels. In particular, we prove that pseudo-labels based on stable features provide sufficient guidance for doing so, provided that stable and unstable features are conditionally independent given the label. Based on this theoretical insight, we propose Stable Feature Boosting (SFB), an algorithm for: (i) learning a predictor that separates stable and conditionally-independent unstable features; and (ii) using the stable-feature predictions to adapt the unstable-feature predictions in the test domain. Theoretically, we prove that SFB can learn an asymptotically-optimal predictor without test-domain labels. Empirically, we demonstrate the effectiveness of SFB on real and synthetic data.

翻译：为避免在分布外数据上失败，近年来研究致力于提取与标签在跨域中保持稳定或不变关系的特征，同时摒弃其与标签关系随域变化的“虚假”或不稳定特征。然而，不稳定特征往往携带标签的互补信息，若在测试域中正确使用，可提升性能。我们的主要贡献在于证明无需测试域标签即可学习如何利用这些不稳定特征。具体而言，我们证明：当稳定特征与不稳定特征在给定标签条件下条件独立时，基于稳定特征的伪标签足以指导这一过程。基于这一理论洞见，我们提出**稳定特征增强（SFB）**算法，用于：(i) 学习一个能分离稳定特征及条件独立不稳定特征的预测器；(ii) 在测试域中利用稳定特征预测调整不稳定特征预测。理论上，我们证明SFB可在无测试域标签条件下学习渐进最优预测器。实验上，我们在真实与合成数据上验证了SFB的有效性。