Optimally tackling covariate shift in RKHS-based nonparametric regression. (arXiv:2205.02986v1 [math.ST])

Web: http://arxiv.org/abs/2205.02986

We study the covariate shift problem in the context of nonparametric
regression over a reproducing kernel Hilbert space (RKHS). We focus on two
natural families of covariate shift problems defined using the likelihood
ratios between the source and target distributions. When the likelihood ratios
are uniformly bounded, we prove that the kernel ridge regression (KRR)
estimator with a carefully chosen regularization parameter is minimax
rate-optimal (up to a log factor) for a large family of RKHSs with regular
kernel eigenvalues. …

arxiv math regression