Classification tasks usually assume that all possible classes are present during the training phase. This is restrictive if the algorithm is used over a long time and possibly encounters samples from unknown new classes. It is therefore fundamental to develop algorithms able to distinguish between normal and abnormal test data. In the last few years, extreme value theory has become an important tool in multivariate statistics and machine learning. The recently introduced extreme value machine, a classifier motivated by extreme value theory, addresses this problem and achieves competitive performance in specific cases. We show that this algorithm has some theoretical and practical drawbacks and can fail even if the recognition task is fairly simple. To overcome these limitations, we propose two new algorithms for anomaly detection relying on approximations from extreme value theory that are more robust in such cases. We exploit the intuition that test points that are extremely far from the training classes are more likely to be abnormal objects. We derive asymptotic results motivated by univariate extreme value theory that make this intuition precise. We show the effectiveness of our classifiers in simulations and on real data sets.

分类任务通常假定在培训阶段中存在所有可能的课程。如果该算法使用了很长时间，并且可能遇到来自未知新类的样本，则这是限制性的。因此，开发能够区分正常和异常测试数据的算法至关重要。在最近几年中，极值理论已成为多元统计和机器学习中的重要工具。最近引入的极限值机器（一种基于极限值理论的分类器）解决了这个问题，并在特定情况下实现了竞争优势。我们表明，该算法具有一些理论和实践上的缺陷，即使识别任务相当简单，也可能会失败。为了克服这些限制，我们提出了两种新的异常检测算法，这些算法依赖于极值理论的近似值，在这种情况下更为稳健。我们利用这样的直觉，即离培训课程极远的测试点更有可能是异常对象。我们得出由单变量极值理论推动的渐近结果，这些结果使这种直觉变得精确。我们在模拟和真实数据集上显示了分类器的有效性。