Theoretical Performance Guarantees for Partial Domain Adaptation via Partial Optimal Transport
This work addresses the problem of partial domain adaptation for machine learning practitioners by providing a theoretical foundation for heuristic methods, though it is incremental as it builds on existing PDA frameworks.
The paper tackles the lack of theoretical guarantees in partial domain adaptation (PDA) by deriving generalization bounds based on partial optimal transport, which validate using the partial Wasserstein distance for domain alignment and provide theoretically motivated weights for source loss. The result is a practical algorithm, WARMPOT, that shows competitive performance in experiments and improves on existing weighting schemes.
In many scenarios of practical interest, labeled data from a target distribution are scarce while labeled data from a related source distribution are abundant. One particular setting of interest arises when the target label space is a subset of the source label space, leading to the framework of partial domain adaptation (PDA). Typical approaches to PDA involve minimizing a domain alignment term and a weighted empirical loss on the source data, with the aim of transferring knowledge between domains. However, a theoretical basis for this procedure is lacking, and in particular, most existing weighting schemes are heuristic. In this work, we derive generalization bounds for the PDA problem based on partial optimal transport. These bounds corroborate the use of the partial Wasserstein distance as a domain alignment term, and lead to theoretically motivated explicit expressions for the empirical source loss weights. Inspired by these bounds, we devise a practical algorithm for PDA, termed WARMPOT. Through extensive numerical experiments, we show that WARMPOT is competitive with recent approaches, and that our proposed weights improve on existing schemes.