Generalization Analysis for Classification on Korobov Space

Abstract: In this paper, the classification algorithm arising from Tikhonov regularization is discussed. The main intention is to derive learning rates for the excess misclassification error according to the convex $\eta$-norm loss function $\phi(v)=(1 - v)_{+}^{\eta}$, $\eta\geq1$. Following the argument, the estimation of error under Tsybakov noise conditions is studied. In addition, we propose the rate of $L_p$ approximation of functions from Korobov space $X^{2, p}([-1,1]^{d})$, $1\leq p \leq \infty$, by the shallow ReLU neural network. This result consists of a novel Fourier analysis