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 model accordingly. Our non-asymptotic excess risk bounds show that in quite general scenarios, our estimator adapts to the structure of the target distribution as well as the covariate shift. It achieves the minimax optimal error rate up to a logarithmic factor. The use of pseudo-labels in model selection does not have major negative impacts.

翻译：我们研究并分析了一种在协变量偏移下进行核岭回归的原则性方法。目标是在目标分布上基于该分布的无标签数据以及可能具有不同特征分布的有标签数据，学习一个均方误差较小的回归函数。我们提出将有标签数据分为两部分，分别进行核岭回归，从而获得一组候选模型和一个插补模型。利用后者填补缺失标签，并据此选择最佳候选模型。我们的非渐近过剩风险界表明，在相当一般的情景下，我们的估计器能够适应目标分布的结构以及协变量偏移。它达到了最小最大最优误差率（至多相差一个对数因子）。在模型选择中使用伪标签不会产生显著的负面影响。