As a prominent challenge in addressing real-world issues within a dynamic environment, label shift, which refers to the learning setting where the source (training) and target (testing) label distributions do not match, has recently received increasing attention. Existing label shift methods solely use unlabeled target samples to estimate the target label distribution, and do not involve them during the classifier training, resulting in suboptimal utilization of available information. One common solution is to directly blend the source and target distributions during the training of the target classifier. However, we illustrate the theoretical deviation and limitations of the direct distribution mixture in the label shift setting. To tackle this crucial yet unexplored issue, we introduce the concept of aligned distribution mixture, showcasing its theoretical optimality and generalization error bounds. By incorporating insights from generalization theory, we propose an innovative label shift framework named as Aligned Distribution Mixture (ADM). Within this framework, we enhance four typical label shift methods by introducing modifications to the classifier training process. Furthermore, we also propose a one-step approach that incorporates a pioneering coupling weight estimation strategy. Considering the distinctiveness of the proposed one-step approach, we develop an efficient bi-level optimization strategy. Experimental results demonstrate the effectiveness of our approaches, together with their effectiveness in COVID-19 diagnosis applications.

翻译：作为在动态环境中解决现实世界问题的一个突出挑战，标签偏移——即源域（训练）与目标域（测试）标签分布不匹配的学习场景——近年来受到越来越多的关注。现有的标签偏移方法仅使用未标记的目标样本来估计目标标签分布，而未在分类器训练过程中利用这些样本，导致对可用信息的利用不够充分。一种常见的解决方案是在训练目标分类器时直接混合源域和目标域的分布。然而，我们阐述了在标签偏移场景下直接进行分布混合的理论偏差与局限性。为了应对这一重要但尚未被充分探索的问题，我们引入了对齐分布混合的概念，并展示了其理论最优性及泛化误差界。通过结合泛化理论的见解，我们提出了一种名为对齐分布混合（ADM）的创新性标签偏移框架。在此框架内，我们通过改进分类器的训练过程，对四种典型的标签偏移方法进行了增强。此外，我们还提出了一种一步式方法，该方法引入了一种开创性的耦合权重估计策略。考虑到所提出的一步式方法的独特性，我们开发了一种高效的双层优化策略。实验结果证明了我们方法的有效性，及其在COVID-19诊断应用中的良好表现。