Covariate shift in Hilbert space: A solution via surrogate kernels

Covariate shift is an unconventional learning scenario in which training and testing data have different distributions. A general principle to solve the problem is to make the training data distribution similar to that of the test domain, such that classifiers computed on the former generalize well to the latter. Current approaches typically target on sample distributions in the input space, however, for kernel-based learning methods, the algorithm performance depends directly on the geometry of the kernel-induced feature space. Motivated by this, we propose to match data distributions in the Hilbert space, which, given a pre-defined empirical kernel map, can be formulated as aligning kernel matrices across domains. In particular, to evaluate similarity of kernel matrices defined on arbitrarily different samples, the novel concept of surrogate kernel is introduced based on the Mercer's theorem. Our approach caters the model adaptation specifically to kernel-based learning mechanism, and demonstrates promising results on several real-world applications.