A linear time method for the detection of point and collective anomalies

TL;DR

This paper introduces CAPA, a fast and accurate method for detecting both point and collective anomalies in data sequences, especially those characterized by changes in mean or variance.

Contribution

The paper presents CAPA, a novel computationally efficient approach that distinguishes collective anomalies from point anomalies and proves its consistency theoretically.

Findings

CAPA has near-linear computational complexity.

CAPA outperforms existing methods in detecting and locating collective anomalies.

CAPA successfully detects exoplanets from Kepler telescope data.

Abstract

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.