The anomaly detection method presented by this article has a special feature: it not only indicates whether or not an observation is anomalous but also tells what exactly makes an anomalous observation unusual. Hence, it provides support to localize the reason of the anomaly. The proposed approach is model based; it relies on the multivariate probability distribution associated with the observations. Since the rare events are present in the tails of the probability distributions, we use copula functions, which are able to model the fat-tailed distributions well. The presented procedure scales well; it can cope with a large number of high-dimensional samples. Furthermore, our procedure can cope with missing values as well, which occur frequently in high-dimensional datasets. In the second part of the article, we demonstrate the usability of the method through a case study, where we analyze a large dataset consisting of the performance counters of a real mobile telecommunication network. Since such networks are complex systems, the signs of sub-optimal operation can remain hidden for a potentially long time. With the proposed procedure, many such hidden issues can be isolated and indicated to the network operator.

中文翻译：

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大规模、高维连续数据的基于 Copula 的异常评分和定位

本文提出的异常检测方法有一个特殊的特点：它不仅可以指示观察是否异常，而且还可以说明究竟是什么使异常观察变得异常。因此，它为定位异常原因提供了支持。建议的方法是基于模型的；它依赖于与观察相关的多元概率分布。由于罕见事件存在于概率分布的尾部，因此我们使用能够很好地模拟肥尾分布的 copula 函数。所提出的程序可以很好地扩展；它可以应对大量的高维样本。此外，我们的程序也可以处理缺失值，这在高维数据集中经常出现。在文章的第二部分，我们通过案例研究展示了该方法的可用性，我们分析了一个由真实移动电信网络的性能计数器组成的大型数据集。由于此类网络是复杂的系统，次优操作的迹象可能会隐藏很长时间。使用所提出的程序，许多此类隐藏的问题可以被隔离并指示给网络运营商。