Towards a Unified Analysis of Kernel-based Methods Under Covariate Shift
This work addresses covariate shift, a common issue in real-world data where input distributions differ between source and target domains, providing a theoretical foundation for various learning tasks, though it is incremental as it builds on existing kernel-based methods.
The paper tackles the problem of covariate shift in machine learning by proposing a unified theoretical analysis for nonparametric methods in reproducing kernel Hilbert spaces, establishing sharp convergence rates for a general loss function that matches optimal results from literature.
Covariate shift occurs prevalently in practice, where the input distributions of the source and target data are substantially different. Despite its practical importance in various learning problems, most of the existing methods only focus on some specific learning tasks and are not well validated theoretically and numerically. To tackle this problem, we propose a unified analysis of general nonparametric methods in a reproducing kernel Hilbert space (RKHS) under covariate shift. Our theoretical results are established for a general loss belonging to a rich loss function family, which includes many commonly used methods as special cases, such as mean regression, quantile regression, likelihood-based classification, and margin-based classification. Two types of covariate shift problems are the focus of this paper and the sharp convergence rates are established for a general loss function to provide a unified theoretical analysis, which concurs with the optimal results in literature where the squared loss is used. Extensive numerical studies on synthetic and real examples confirm our theoretical findings and further illustrate the effectiveness of our proposed method.