A linear time method for the detection of point and collective anomalies
This addresses the need for efficient anomaly detection in applications like astronomy, though it is incremental as it builds on existing statistical methods.
The paper tackles the problem of detecting both point and collective anomalies in data sequences, introducing the CAPA method which achieves close to linear computational cost and higher accuracy in detecting and locating collective anomalies compared to other approaches.
The challenge of efficiently identifying anomalies in data sequences is an important statistical problem that now arises in many applications. Whilst 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 characterised by either a change in mean, variance, or both, and distinguishes them from point anomalies. Theoretical results establish the consistency of CAPA at detecting collective anomalies and, as a by-product, the consistency of a popular penalised cost based change in mean and variance detection method. 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.