Kernel machines with missing covariates

We develop a family of doubly robust kernel machines for classification in the presence of missing covariates. We assume that the missingness is missing at random and the missing pattern is homogeneous over a subset of covariates. First, we construct a novel convex augmented loss function using inverse probability weighting, multiple imputation, and surrogacy. It features (i) the double robustness against misspecification of the missing mechanism or the imputation model, and (ii) computation feasibility via a constrained quadratic optimization. Second, we obtain theoretical results for the proposed kernel machine, which include Fisher consistency, an upper bound of the excess risk, and the rate of convergence. We demonstrate the finite sample performance of the proposed kernel machine through simulation and real data analysis.