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

Understand

We prove bounds for the approximation and estimation of certain binary 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 dimensionality can be overcome in this setting; in fact, the input dimension only enters in the form of a polynomial factor.
• Regarding the regularity of the target classification function, we assume the interfaces between the different classes to be locally of Barron-type.