Class Probability Matching Using Kernel Methods for Label Shift
  Adaptation
Hongwei Wen Annika Betken Hanyuan Hang
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.