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High‐dimensional, multiscale online changepoint detection

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  • Yudong Chen
  • Tengyao Wang
  • Richard J. Samworth

Abstract

We introduce a new method for high‐dimensional, online changepoint detection in settings where a p‐variate Gaussian data stream may undergo a change in mean. The procedure works by performing likelihood ratio tests against simple alternatives of different scales in each coordinate, and then aggregating test statistics across scales and coordinates. The algorithm is online in the sense that both its storage requirements and worst‐case computational complexity per new observation are independent of the number of previous observations; in practice, it may even be significantly faster than this. We prove that the patience, or average run length under the null, of our procedure is at least at the desired nominal level, and provide guarantees on its response delay under the alternative that depend on the sparsity of the vector of mean change. Simulations confirm the practical effectiveness of our proposal, which is implemented in the R package ocd, and we also demonstrate its utility on a seismology data set.

Suggested Citation

  • Yudong Chen & Tengyao Wang & Richard J. Samworth, 2022. "High‐dimensional, multiscale online changepoint detection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 234-266, February.
    • Handle: RePEc:bla:jorssb:v:84:y:2022:i:1:p:234-266
    DOI: 10.1111/rssb.12447
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    References listed on IDEAS

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    1. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.
    2. 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.
    3. Rafal Baranowski & Yining Chen & Piotr Fryzlewicz, 2019. "Narrowest‐over‐threshold detection of multiple change points and change‐point‐like features," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 649-672, July.
    4. Tengyao Wang & Richard J. Samworth, 2018. "High dimensional change point estimation via sparse projection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 57-83, January.
    5. Y. Mei, 2010. "Efficient scalable schemes for monitoring a large number of data streams," Biometrika, Biometrika Trust, vol. 97(2), pages 419-433.
    6. Achim Zeileis & Friedrich Leisch & Christian Kleiber & Kurt Hornik, 2005. "Monitoring structural change in dynamic econometric models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(1), pages 99-121, January.
    7. Leisch, Friedrich & Hornik, Kurt & Kuan, Chung-Ming, 2000. "Monitoring Structural Changes With The Generalized Fluctuation Test," Econometric Theory, Cambridge University Press, vol. 16(6), pages 835-854, December.
    8. Lajos Horváth & Gregory Rice, 2014. "Rejoinder on: Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 287-290, June.
    9. Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-1065, September.
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    Cited by:

    1. Follain, Bertille & Wang, Tengyao & Samworth, Richard J., 2022. "High-dimensional changepoint estimation with heterogeneous missingness," LSE Research Online Documents on Economics 115014, London School of Economics and Political Science, LSE Library.
    2. Tuomas Rajala & Petteri Packalen & Mari Myllymäki & Annika Kangas, 2023. "Improving Detection of Changepoints in Short and Noisy Time Series with Local Correlations: Connecting the Events in Pixel Neighbourhoods," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(3), pages 564-590, September.
    3. Yu Jeffrey Hu & Jeroen Rombouts & Ines Wilms, 2023. "Fast Forecasting of Unstable Data Streams for On-Demand Service Platforms," Papers 2303.01887, arXiv.org, revised May 2024.

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