Many existing covariate shift adaptation methods estimate sample weights given to loss values to mitigate the gap between the source and the target distribution. However, estimating the optimal weights typically involves computationally expensive matrix inversion and hyper-parameter tuning. In this paper, we propose a new covariate shift adaptation method which avoids estimating the weights. The basic idea is to directly work on unlabeled target data, labeled according to the $k$-nearest neighbors in the source dataset. Our analysis reveals that setting $k = 1$ is an optimal choice. This property removes the necessity of tuning the only hyper-parameter $k$ and leads to a running time quasi-linear in the sample size. Our results include sharp rates of convergence for our estimator, with a tight control of the mean square error and explicit constants. In particular, the variance of our estimators has the same rate of convergence as for standard parametric estimation despite their non-parametric nature. The proposed estimator shares similarities with some matching-based treatment effect estimators used, e.g., in biostatistics, econometrics, and epidemiology. Our experiments show that it achieves drastic reduction in the running time with remarkable accuracy.

翻译：许多现有的协变量偏移适应方法通过估计赋予损失值的样本权重来缓解源分布与目标分布之间的差异。然而，估计最优权重通常涉及计算成本高昂的矩阵求逆和超参数调优。本文提出一种新的协变量偏移适应方法，该方法无需估计权重。其基本思想是直接基于源数据集中$k$个最近邻的标记信息对未标记的目标数据进行标注。我们的分析表明，设置$k = 1$是最优选择。这一特性消除了调整唯一超参数$k$的必要性，并使得算法运行时间与样本量呈拟线性关系。我们的研究结果包括所提出估计量的收敛速率精确分析，其中均方误差得到严格控制且常数项显式表达。特别值得注意的是，尽管该估计量具有非参数特性，其方差收敛速率与标准参数估计相同。所提出的估计量与生物统计学、计量经济学和流行病学等领域中基于匹配的处理效应估计方法具有相似性。实验结果表明，该方法在保持卓越精度的同时实现了运行时间的显著降低。