Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithm

arXiv:2312.07186v3 Announce Type: replace-cross
Abstract: We present the first optimal rates for infinite-dimensional vector-valued ridge regression on a continuous scale of norms that interpolate between $L_2$ and the hypothesis space, which we consider as a vector-valued reproducing kernel Hilbert space. These rates allow to treat the misspecified case in which the true regression function is not contained in the hypothesis space. We combine standard assumptions on the capacity of the hypothesis space with a novel tensor product construction of vector-valued …

abstract algorithm arxiv case continuous cs.lg hypothesis kernel least norm regression ridge scale space squares stat.ml type vector