Class Probability Matching Using Kernel Methods for Label Shift Adaptation
This addresses label shift adaptation for domain adaptation tasks, offering a more natural approach than feature-based methods, but it is incremental as it builds on existing adaptation frameworks.
The paper tackles label shift adaptation in domain adaptation by proposing a class probability matching (CPM) framework that matches class probability functions on the label space, and introduces CPMKM using kernel methods. The result shows that CPMKM outperforms existing algorithms on real datasets with established theoretical convergence rates.
In domain adaptation, covariate shift and label shift problems are two distinct and complementary tasks. In covariate shift adaptation where the differences in data distribution arise from variations in feature probabilities, existing approaches naturally address this problem based on \textit{feature probability matching} (\textit{FPM}). However, for label shift adaptation where the differences in data distribution stem solely from variations in class probability, current methods still use FPM on the $d$-dimensional feature space to estimate the class probability ratio on the one-dimensional label space. To address label shift adaptation more naturally and effectively, inspired by a new representation of the source domain's class probability, we propose a new framework called \textit{class probability matching} (\textit{CPM}) which matches two class probability functions on the one-dimensional label space to estimate the class probability ratio, fundamentally different from FPM operating on the $d$-dimensional feature space. Furthermore, by incorporating the kernel logistic regression into the CPM framework to estimate the conditional probability, we propose an algorithm called \textit{class probability matching using kernel methods} (\textit{CPMKM}) for label shift adaptation. From the theoretical perspective, we establish the optimal convergence rates of CPMKM with respect to the cross-entropy loss for multi-class label shift adaptation. From the experimental perspective, comparisons on real datasets demonstrate that CPMKM outperforms existing FPM-based and maximum-likelihood-based algorithms.