Generalization Analysis for Classification on Korobov Space
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Abstract (arXiv)
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≥1. Following the argument, the estimation of error under Tsybakov noise conditions is studied. In addition, we propose the rate of Lp approximation of functions from Korobov space X2, p([-1,1]d), 1≤ p ≤ ∞, by the shallow ReLU neural network. This result consists of a novel Fourier analysis
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References · 6
- 2016Error bounds for approximations with deep ReLU networkscited by 574
- 2016Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with ℓ1 and ℓ0 Controlscited by 84
- 2015Provable approximation properties for deep neural networkscited by 60
- 2021Theory of Deep Convolutional Neural Networks III: Approximating Radial Functionscited by 22
- 2023Rates of Approximation by ReLU Shallow Neural Networkscited by 12
- 2023Approximation of Nonlinear Functionals Using Deep ReLU Networkscited by 8
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