用极值理论量化神经网络的大误差，更准确评估模型可靠性。
Accuracy estimation of neural networks by extreme value theory
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神经网络能够逼近紧集上的任意连续函数，但其误差（函数与网络输出间的剩余偏差）难以量化。本文提出应用极值理论来刻画大误差，这些误差在实际应用中尤为重要。当误差超过某一阈值时，其分布近似为广义帕累托分布。我们提出一种新的形状参数估计器，适用于描述神经网络的误差特性。文中提供了数值实验验证方法有效性。
原文摘要 · Abstract (English)
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.
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