The challenge of efficiently identifying anomalies in data sequences is an important statistical problem that now arises in many applications. Although there has been substantial work aimed at making statistical analyses robust to outliers, or point anomalies, there has been much less work on detecting anomalous segments, or collective anomalies, particularly in those settings where point anomalies might also occur. In this article, we introduce collective and point anomalies (CAPA), a computationally efficient approach that is suitable when collective anomalies are characterized by either a change in mean, variance, or both, and distinguishes them from point anomalies. Empirical results show that CAPA has close to linear computational cost as well as being more accurate at detecting and locating collective anomalies than other approaches. We demonstrate the utility of CAPA through its ability to detect exoplanets from light curve data from the Kepler telescope and its capacity to detect machine faults from temperature data.

中文翻译：

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一种用于检测集体和点异常的线性时间方法

有效识别数据序列中的异常是一个重要的统计问题，现在在许多应用中都出现了。尽管有大量工作旨在使统计分析对异常值或点异常具有鲁棒性，但在检测异常段或集体异常方面的工作要少得多，特别是在那些也可能发生点异常的环境中。在本文中，我们介绍了集体和点异常 (CAPA)，这是一种计算有效的方法，适用于集体异常的特征是均值、方差或两者的变化，并将它们与点异常区分开来。实证结果表明，CAPA 具有接近线性的计算成本，并且在检测和定位集体异常方面比其他方法更准确。