Supervised learning is often affected by a covariate shift in which the
marginal distributions of instances (covariates $x$) of training and testing
samples $\mathrm{p}_\text{tr}(x)$ and $\mathrm{p}_\text{te}(x)$ are different
but the label conditionals coincide. Existing approaches address such covariate
shift by either using the ratio
$\mathrm{p}_\text{te}(x)/\mathrm{p}_\text{tr}(x)$ to weight training samples
(reweighting methods) or using the ratio
$\mathrm{p}_\text{tr}(x)/\mathrm{p}_\text{te}(x)$ to weight testing samples
(robust methods). However, the performance of such approaches can be poor under
support mismatch or when the above ratios take large values. We propose a
minimax risk classification (MRC) approach for covariate shift adaptation that
avoids such limitations by weighting both training and testing samples. In
addition, we develop effective techniques that obtain both sets of weights and
generalize the conventional kernel mean matching method. We provide novel
generalization bounds for our method that show a significant increase in the
effective sample size compared with reweighted methods. The proposed method
also achieves enhanced classification performance in both synthetic and
empirical experiments.

该研究提出了最小化风险分类的方法来处理资料控制变量变化的问题，同时也发展了有效的技术，取得了更好的分类性能。

协变量偏移适应性的双加权方法

Double-Weighting for Covariate Shift Adaptation

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.

针对一种特定的协变量偏移问题，该研究利用核均值匹配 (KMM) 估计器的高概率置信界推导出该估计器的收敛速率，并与自然插值估计器进行比较，结果表明其具有更好的效果和应用价值。

核均值匹配在协变量转移下的分析

Analysis of Kernel Mean Matching under Covariate Shift

This paper presents a theoretical analysis of sample selection bias
correction. The sample bias correction technique commonly used in machine
learning consists of reweighting the cost of an error on each training point of
a biased sample to more closely reflect the unbiased distribution. This relies
on weights derived by various estimation techniques based on finite samples. We
analyze the effect of an error in that estimation on the accuracy of the
hypothesis returned by the learning algorithm for two estimation techniques: a
cluster-based estimation technique and kernel mean matching. We also report the
results of sample bias correction experiments with several data sets using
these techniques. Our analysis is based on the novel concept of distributional
stability which generalizes the existing concept of point-based stability. Much
of our work and proof techniques can be used to analyze other importance
weighting techniques and their effect on accuracy when using a distributionally
stable algorithm.

本文基于分布稳定性的新概念，对样本选择偏差校正进行了理论分析，研究了两种估计技术：基于簇的估计技术和核均值匹配，以及使用这些技术对几个数据集进行样本偏差校正实验。