Analysis of Kernel Mean Matching under Covariate Shift
This work addresses covariate shift, a common issue in real-world supervised learning, providing theoretical evidence for KMM's effectiveness, though it appears incremental as it builds on existing methods.
The paper tackles the problem of covariate shift in supervised learning by deriving high probability confidence bounds for the kernel mean matching (KMM) estimator, showing its convergence rate depends on regression function regularity and kernel capacity, and establishes KMM's superiority over a plug-in estimator.
In real supervised learning scenarios, it is not uncommon that the training and test sample follow different probability distributions, thus rendering the necessity to correct the sampling bias. Focusing on a particular covariate shift problem, we derive high probability confidence bounds for the kernel mean matching (KMM) estimator, whose convergence rate turns out to depend on some regularity measure of the regression function and also on some capacity measure of the kernel. By comparing KMM with the natural plug-in estimator, we establish the superiority of the former hence provide concrete evidence/understanding to the effectiveness of KMM under covariate shift.