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Seeded binary segmentation: a general methodology for fast and optimal changepoint detection

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  • S Kovács
  • P Bühlmann
  • H Li
  • A Munk

Abstract

SummaryWe propose seeded binary segmentation for large-scale changepoint detection problems. We construct a deterministic set of background intervals, called seeded intervals, in which single changepoint candidates are searched for. The final selection of changepoints based on these candidates can be done in various ways, adapted to the problem at hand. The method is thus easy to adapt to many changepoint problems, ranging from univariate to high dimensional. Compared to recently popular random background intervals, seeded intervals lead to reproducibility and much faster computations. For the univariate Gaussian change in mean set-up, the methodology is shown to be asymptotically minimax optimal when paired with appropriate selection criteria. We demonstrate near-linear runtimes and competitive finite sample estimation performance. Furthermore, we illustrate the versatility of our method in high-dimensional settings.

Suggested Citation

  • S Kovács & P Bühlmann & H Li & A Munk, 2023. "Seeded binary segmentation: a general methodology for fast and optimal changepoint detection," Biometrika, Biometrika Trust, vol. 110(1), pages 249-256.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:1:p:249-256.
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    File URL: http://hdl.handle.net/10.1093/biomet/asac052
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    References listed on IDEAS

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    1. Klaus Frick & Axel Munk & Hannes Sieling, 2014. "Multiscale change point inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 495-580, June.
    2. Fryzlewicz, Piotr, 2020. "Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection—rejoinder," LSE Research Online Documents on Economics 106681, London School of Economics and Political Science, LSE Library.
    3. Fryzlewicz, Piotr, 2020. "Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection," LSE Research Online Documents on Economics 103430, London School of Economics and Political Science, LSE Library.
    4. Florian Pein & Hannes Sieling & Axel Munk, 2017. "Heterogeneous change point inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1207-1227, September.
    5. Haeran Cho & Claudia Kirch, 2022. "Two-stage data segmentation permitting multiscale change points, heavy tails and dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 653-684, August.
    6. Kim, Chang-Jin & Morley, James C. & Nelson, Charles R., 2005. "The Structural Break in the Equity Premium," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 181-191, April.
    7. Camilo Rivera & Guenther Walther, 2013. "Optimal detection of a jump in the intensity of a Poisson process or in a density with likelihood ratio statistics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 752-769, December.
    8. Nancy R. Zhang & David O. Siegmund, 2007. "A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data," Biometrics, The International Biometric Society, vol. 63(1), pages 22-32, March.
    9. Fryzlewicz, Piotr, 2014. "Wild binary segmentation for multiple change-point detection," LSE Research Online Documents on Economics 57146, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Cho, Haeran & Fryzlewicz, Piotr, 2023. "Multiple change point detection under serial dependence: wild contrast maximisation and gappy Schwarz algorithm," LSE Research Online Documents on Economics 120085, London School of Economics and Political Science, LSE Library.
    2. Florian Gunsilius & David Van Dijcke, 2023. "Free Discontinuity Regression: With an Application to the Economic Effects of Internet Shutdowns," Papers 2309.14630, arXiv.org, revised Jan 2024.

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