  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.
