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.

通过重新加权样本，本研究在再生核希尔伯特空间中修正最小二乘学习算法的误差，以解决未来数据分布与训练数据分布不同引起的问题，并证明在弱平滑条件下，相比现有分析所证明的，为了达到与标准监督学习相同精度所需的样本数量更小。