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 $\hat{I}\cdot$-norm loss function $\ddot{I}•(v)=(1-v{)}_{+}^{\hat{I}}\cdot$, $\hat{I}\cdot \ge 1$. 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 $X^{2,p}([-1,1{]}^d)$, $1\le p\le \infty$, by the shallow ReLU neural network. This result consists of a novel Fourier analysis