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Changepoint Detection in the Presence of Outliers

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  • Paul Fearnhead
  • Guillem Rigaill

Abstract

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 suitable—as 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.

Suggested Citation

  • Paul Fearnhead & Guillem Rigaill, 2019. "Changepoint Detection in the Presence of Outliers," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 169-183, January.
  • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:525:p:169-183
    DOI: 10.1080/01621459.2017.1385466
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    Cited by:

    1. Kang-Ping Lu & Shao-Tung Chang, 2023. "An Advanced Segmentation Approach to Piecewise Regression Models," Mathematics, MDPI, vol. 11(24), pages 1-23, December.
    2. Haoran Lu & Dianpeng Wang, 2024. "Grouped Change-Points Detection and Estimation in Panel Data," Mathematics, MDPI, vol. 12(5), pages 1-20, March.
    3. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    4. Lee, Sangyeol & Meintanis, Simos G. & Pretorius, Charl, 2022. "Monitoring procedures for strict stationarity based on the multivariate characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    5. Ricardo C. Pedroso & Rosangela H. Loschi & Fernando Andrés Quintana, 2023. "Multipartition model for multiple change point identification," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 759-783, June.
    6. Jinhua Wu & Can Wang & Xiong He & Chunshan Zhou & Hongwei Wang, 2024. "Nonlinear Effects of Land-Use Conflicts in Xinjiang: Critical Thresholds and Implications for Optimal Zoning," Land, MDPI, vol. 13(5), pages 1-24, May.
    7. Lazar, Emese & Wang, Shixuan & Xue, Xiaohan, 2023. "Loss function-based change point detection in risk measures," European Journal of Operational Research, Elsevier, vol. 310(1), pages 415-431.
    8. Lu Shaochuan, 2023. "Scalable Bayesian Multiple Changepoint Detection via Auxiliary Uniformisation," International Statistical Review, International Statistical Institute, vol. 91(1), pages 88-113, April.
    9. Muhammad Zafran Muhammad Zaly Shah & Anazida Zainal & Taiseer Abdalla Elfadil Eisa & Hashim Albasheer & Fuad A. Ghaleb, 2023. "A Semisupervised Concept Drift Adaptation via Prototype-Based Manifold Regularization Approach with Knowledge Transfer," Mathematics, MDPI, vol. 11(2), pages 1-30, January.
    10. Trevor Harris & Bo Li & J. Derek Tucker, 2022. "Scalable multiple changepoint detection for functional data sequences," Environmetrics, John Wiley & Sons, Ltd., vol. 33(2), March.
    11. Hajra Siddiqa & Sajid Ali & Ismail Shah, 2021. "Most recent changepoint detection in censored panel data," Computational Statistics, Springer, vol. 36(1), pages 515-540, March.
    12. Kang-Ping Lu & Shao-Tung Chang, 2022. "Robust Switching Regressions Using the Laplace Distribution," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    13. Kang-Ping Lu & Shao-Tung Chang, 2021. "Robust Algorithms for Change-Point Regressions Using the t -Distribution," Mathematics, MDPI, vol. 9(19), pages 1-28, September.

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