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Recent work has highlighted the label alignment property (LAP) in supervisedlearning, where the vector of all labels in the dataset is mostly in the spanof the top few singular vectors of the data matrix. Drawing inspiration fromthis observation, we propose a regularization method for unsupervised domainadaptation that encourages alignment between the predictions in the targetdomain and its top singular vectors. Unlike conventional domain adaptationapproaches that focus on regularizing representations, we instead regularizethe classifier to align with the unsupervised target data, guided by the LAP inboth the source and target domains. Theoretical analysis demonstrates that,under certain assumptions, our solution resides within the span of the topright singular vectors of the target domain data and aligns with the optimalsolution. By removing the reliance on the commonly used optimal joint riskassumption found in classic domain adaptation theory, we showcase theeffectiveness of our method on addressing problems where traditional domainadaptation methods often fall short due to high joint error. Additionally, wereport improved performance over domain adaptation baselines in well-knowntasks such as MNIST-USPS domain adaptation and cross-lingual sentimentanalysis.

Label Alignment Regularization for Distribution Shift