A Unified Joint Maximum Mean Discrepancy for Domain Adaptation
This work addresses a theoretical bottleneck in domain adaptation for machine learning practitioners, offering incremental improvements in handling imbalanced datasets and label distribution shifts.
The paper tackles the challenge of efficiently optimizing joint probability distribution distances in domain adaptation by deriving a unified form of Joint Maximum Mean Discrepancy (JMMD) that simplifies optimization and generalizes existing distances, and demonstrates its effectiveness through experiments on cross-domain datasets with improved performance metrics.
Domain adaptation has received a lot of attention in recent years, and many algorithms have been proposed with impressive progress. However, it is still not fully explored concerning the joint probability distribution (P(X, Y)) distance for this problem, since its empirical estimation derived from the maximum mean discrepancy (joint maximum mean discrepancy, JMMD) will involve complex tensor-product operator that is hard to manipulate. To solve this issue, this paper theoretically derives a unified form of JMMD that is easy to optimize, and proves that the marginal, class conditional and weighted class conditional probability distribution distances are our special cases with different label kernels, among which the weighted class conditional one not only can realize feature alignment across domains in the category level, but also deal with imbalance dataset using the class prior probabilities. From the revealed unified JMMD, we illustrate that JMMD degrades the feature-label dependence (discriminability) that benefits to classification, and it is sensitive to the label distribution shift when the label kernel is the weighted class conditional one. Therefore, we leverage Hilbert Schmidt independence criterion and propose a novel MMD matrix to promote the dependence, and devise a novel label kernel that is robust to label distribution shift. Finally, we conduct extensive experiments on several cross-domain datasets to demonstrate the validity and effectiveness of the revealed theoretical results.