A priori estimates for classification problems using neural networks

TL;DR

This paper derives theoretical a priori error estimates for neural network classifiers in binary and multi-class settings using Rademacher complexity and approximation theorems.

Contribution

It introduces a method to obtain error bounds for neural network classifiers based on complexity measures and approximation properties.

Findings

Provides explicit a priori error bounds for neural network classifiers.

Connects Rademacher complexity with approximation capabilities of neural networks.

Offers theoretical insights into the generalization performance of neural networks.

Abstract

We consider binary and multi-class classification problems using hypothesis classes of neural networks. For a given hypothesis class, we use Rademacher complexity estimates and direct approximation theorems to obtain a priori error estimates for regularized loss functionals.