To avoid failures on out-of-distribution data, recent works have sought to extract features that have an invariant or stable relationship with the label across domains, discarding "spurious" or unstable features whose relationship with the label changes across domains. However, unstable features often carry complementary information that could boost performance if used correctly in the test domain. In this work, we show how this can be done without test-domain 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，近期的研究致力于提取与标签在领域间具有不变或稳定关系的特征，而舍弃那些与标签关系随领域变化的"虚假"或不稳定特征。然而，不稳定特征往往携带补充性信息，若在测试领域得到正确利用，可提升模型性能。在本工作中，我们展示了如何无需测试领域标签实现这一目标。具体而言，我们证明基于稳定特征的伪标签能为该过程提供充分指导，前提是稳定特征与不稳定特征在给定标签条件下保持条件独立。基于这一理论洞见，我们提出稳定特征增强算法（SFB），该算法能够：（i）学习一个可分离稳定特征与条件独立不稳定特征的预测器；（ii）利用稳定特征的预测结果在测试领域调整不稳定特征的预测。理论上，我们证明SFB能在无需测试领域标签的情况下学习渐进最优预测器。实验上，我们通过真实与合成数据验证了SFB的有效性。