Changepoint Detection in the Presence of Outliers

• 成果类型: Article
• 署名作者: Fearnhead, Paul; Rigaill, Guillem
• 署名单位: Lancaster University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Biology (INSB); INRAE; Universite Paris Saclay; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; INRAE; Ecole Nationale Superieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE)
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2017.1385466
• 发表日期: 2019
• 页码: 169-183
• 关键词: dynamic-programming algorithm; least-squares estimation; change-point; binary segmentation; bayesian-inference; number

摘要

Many traditional methods for identifying changepoints can struggle in the presence of outliers, or when the noise is heavy-tailed. Often they will infer additional changepoints to fit the outliers. To overcome this problem, data often needs to be preprocessed to remove outliers, though this is difficult for applications where the data needs to be analyzed online. We present an approach to changepoint detection that is robust to the presence of outliers. The idea is to adapt existing penalized cost approaches for detecting changes so that they use loss functions that are less sensitive to outliers. We argue that loss functions that are bounded, such as the classical biweight loss, are particularly suitableas we show that only bounded loss functions are robust to arbitrarily extreme outliers. We present an efficient dynamic programming algorithm that can find the optimal segmentation under our penalized cost criteria. Importantly, this algorithm can be used in settings where the data needs to be analyzed online. We show that we can consistently estimate the number of changepoints, and accurately estimate their locations, using the biweight loss function. We demonstrate the usefulness of our approach for applications such as analyzing well-log data, detecting copy number variation, and detecting tampering of wireless devices. Supplementary materials for this article are available online.