Accuracy estimation of neural networks by extreme value theory

TL;DR

This paper introduces a novel method using extreme value theory to estimate the error bounds of neural networks, focusing on large errors that are critical in practical applications.

Contribution

It applies extreme value theory to neural network error estimation and proposes a new estimator for the Pareto distribution's shape parameter.

Findings

Error distribution beyond thresholds approximates a generalized Pareto distribution.

The new estimator effectively characterizes large errors in neural networks.

Numerical experiments validate the approach.

Abstract

Neural networks are able to approximate any continuous function on a compact set. However, it is not obvious how to quantify the error of the neural network, i.e., the remaining bias between the function and the neural network. Here, we propose the application of extreme value theory to quantify large values of the error, which are typically relevant in applications. The distribution of the error beyond some threshold is approximately generalized Pareto distributed. We provide a new estimator of the shape parameter of the Pareto distribution suitable to describe the error of neural networks. Numerical experiments are provided.