On the Optimality of Misspecified Kernel Ridge Regression

Abstract

In the misspecified kernel ridge regression problem, researchers usually assume the underground true function f_^* [H]^s, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) H for some s (0,1). The existing minimax optimal results require \|f_^*\|_L^< which implicitly requires s > _0 where _0 (0,1) is the embedding index, a constant depending on H. Whether the KRR is optimal for all s (0,1) is an outstanding problem lasting for years. In this paper, we show that KRR is minimax optimal for any s (0,1) when the H is a Sobolev RKHS.

Tasks

Reproductions