Machine learning classification methods usually assume that all possible classes are sufficiently present within the training set. Due to their inherent rarities, extreme events are always under-represented and classifiers tailored for predicting extremes need to be carefully designed to handle this under-representation. In this paper, we address the question of how to assess and compare classifiers with respect to their capacity to capture extreme occurrences. This is also related to the topic of scoring rules used in forecasting literature. In this context, we propose and study a risk function adapted to extremal classifiers. The inferential properties of our empirical risk estimator are derived under the framework of multivariate regular variation and hidden regular variation. A simulation study compares different classifiers and indicates their performance with respect to our risk function. To conclude, we apply our framework to the analysis of extreme river discharges in the Danube river basin. The application compares different predictive algorithms and test their capacity at forecasting river discharges from other river stations.

翻译：机器学习分类方法通常假设训练集中所有可能的类别都得到充分体现。然而，由于极端事件固有的稀有性，它们在样本中总是代表性不足，因此需要专门设计用于预测极端事件的分类器以应对这种数据不平衡问题。本文探讨如何评估和比较不同分类器在捕捉极端事件方面的能力，这与预测文献中使用的评分规则主题密切相关。在此背景下，我们提出并研究了一种适用于极值分类器的风险函数。基于多元正则变差与隐正则变差的理论框架，我们推导了经验风险估计量的统计推断性质。通过模拟研究比较了不同分类器的表现，并依据所提出的风险函数评估其性能。最后，我们将该框架应用于多瑙河流域极端河流径流量的分析，比较了不同预测算法，并检验它们根据其他水文站数据预测径流量的能力。