Generalization Analysis for Classification on Korobov Space
This work addresses theoretical generalization bounds for classification algorithms, which is an incremental contribution to statistical learning theory.
The paper tackles the problem of deriving learning rates for classification using Tikhonov regularization with a convex loss function under Tsybakov noise conditions, and proposes a rate for approximating functions from Korobov space using shallow ReLU neural networks, with results based on novel Fourier analysis.
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 $η$-norm loss function $φ(v)=(1 - v)_{+}^η$, $η\geq1$. 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