Kernel machines with missing responses

Abstract

Missing responses is a common type of data where the interested outcomes are not always observed. In this paper, we develop two new kernel machines to handle such a case, which can be used for both regression and classification. The first proposed kernel machine uses $\text{only}$ the complete cases where both response and covariates are observed. It is, however, subject to some assumption limitations. Our second proposed doubly-robust kernel machine overcomes such limitations regardless of the misspecification of either the missing mechanism or the conditional distribution of the response. Theoretical properties, including the oracle inequalities for the excess risk, universal consistency, and learning rates are established. We demonstrate the superiority of the proposed methods to some existing methods by simulation and illustrate their application to a real data set concerning a survey about homeless people.