# Neural network approximation and estimation of classifiers with classification boundary in a Barron class

@article{Caragea2020NeuralNA, title={Neural network approximation and estimation of classifiers with classification boundary in a Barron class}, author={Andrei Caragea and Philipp Christian Petersen and Felix Voigtlaender}, journal={arXiv: Functional Analysis}, year={2020} }

We prove bounds for the approximation and estimation of certain classification functions using ReLU neural networks. Our estimation bounds provide a priori performance guarantees for empirical risk minimization using networks of a suitable size, depending on the number of training samples available. The obtained approximation and estimation rates are independent of the dimension of the input, showing that the curse of dimension can be overcome in this setting; in fact, the input dimension only…

## 17 Citations

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- MathematicsArXiv
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In this paper, we consider Barron functions f : [0 , 1] d → R of smoothness σ > 0, which are functions that can be written as f ( x ) = Z R d F ( ξ ) e 2 πi h x,ξ i dξ with Z R d | F ( ) | · σ < ∞ .…

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