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 and 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.

Short bio: Kaizheng Wang is an assistant professor of Industrial Engineering and Operations Research, and a member of the Data Science Institute at Columbia University. He works at the intersection of machine learning, statistics, and optimization. He received his PhD from Princeton University in 2020.