General regularization in covariate shift adaptation
Duc Hoan Nguyen Sergei V. Pereverzyev Werner Zellinger
Sample reweighting is one of the most widely used methods for correcting the
error of least squares learning algorithms in reproducing kernel Hilbert spaces
(RKHS), that is caused by future data distributions that are different from the
training data distribution. In practical situations, the sample weights are
determined by values of the estimated Radon-Nikod\'ym derivative, of the future
data distribution w.r.t.~the training data distribution. In this work, we
review known error bounds for reweighted kernel regression in RKHS and obtain,
by combination, novel results. We show under weak smoothness conditions, that
the amount of samples, needed to achieve the same order of accuracy as in the
standard supervised learning without differences in data distributions, is
smaller than proven by state-of-the-art analyses.