Pseudo-Labeling for kernel ridge regression under covariate shift
提出一种在协变量偏移下进行核岭回归的伪标签方法，利用未标记目标数据和有标记源数据，通过分割数据、构建候选模型和插补模型来填充缺失标签并选择最佳模型，实现了适应目标分布和协变量偏移的估计，达到最小最大最优误差率。
We develop and analyze a principled approach to kernel ridge regression under covariate shift. The goal is to learn a regression function with small mean squared error over a target distribution, based on unlabeled data from there and labeled data that may have a different feature distribution. We propose to split the labeled data into two subsets, and conduct kernel ridge regression on them separately to obtain a collection of candidate models and an imputation model. We use the latter to fill the missing labels and then select the best candidate accordingly. Our nonasymptotic excess risk bounds demonstrate that our estimator adapts effectively to both the structure of the target distribution and the covariate shift. This adaptation is quantified through a notion of effective sample size that reflects the value of labeled source data for the target regression task. Our estimator achieves the minimax optimal error rate up to a polylogarithmic factor, and we find that using pseudo-labels for model selection does not significantly hinder performance.