Understanding Sub-domain Alignment for Domain Adaptation

In unsupervised domain adaptation (UDA), aligning source and target domains improves the predictive performance of learned models on the target domain. A common methodological improvement in alignment methods is to divide the domains and align sub-domains instead. These sub-domain-based algorithms have demonstrated great empirical success but lack theoretical support. In this work, we establish a rigorous theoretical understanding of the advantages of these methods that have the potential to enhance their overall impact on the field. Our theory uncovers that sub-domain-based methods optimize an error bound that is at least as strong as non-sub-domain-based error bounds and is empirically verified to be much stronger. Furthermore, our analysis indicates that when the marginal weights of sub-domains shift between source and target tasks, the performance of these methods may be compromised. We therefore implement an algorithm to robustify sub-domain alignment for domain adaptation under sub-domain shift, offering a valuable adaptation strategy for future sub-domain-based methods. Empirical experiments validate our theoretical insights, prove the necessity for the proposed adaptation strategy, and demonstrate our algorithm's competitiveness in handling label shift.