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Online Change Points Detection for Linear Dynamical Systems with Finite Sample Guarantees (2311.18769v1)

Published 30 Nov 2023 in cs.LG, cs.SY, eess.SY, and stat.ML

Abstract: The problem of online change point detection is to detect abrupt changes in properties of time series, ideally as soon as possible after those changes occur. Existing work on online change point detection either assumes i.i.d data, focuses on asymptotic analysis, does not present theoretical guarantees on the trade-off between detection accuracy and detection delay, or is only suitable for detecting single change points. In this work, we study the online change point detection problem for linear dynamical systems with unknown dynamics, where the data exhibits temporal correlations and the system could have multiple change points. We develop a data-dependent threshold that can be used in our test that allows one to achieve a pre-specified upper bound on the probability of making a false alarm. We further provide a finite-sample-based bound for the probability of detecting a change point. Our bound demonstrates how parameters used in our algorithm affect the detection probability and delay, and provides guidance on the minimum required time between changes to guarantee detection.

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References (30)
  1. Improved algorithms for linear stochastic bandits. Advances in neural information processing systems, 24, 2011.
  2. Bayesian online changepoint detection. arXiv preprint arXiv:0710.3742, 2007.
  3. Modeling of a small unmanned aerial vehicle. Adv Robot Autom, 4(126):2, 2015.
  4. Change point detection via multivariate singular spectrum analysis. Advances in Neural Information Processing Systems, 34:23218–23230, 2021.
  5. A survey of methods for time series change point detection. Knowledge and information systems, 51(2):339–367, 2017.
  6. Data-efficient minimax quickest change detection with composite post-change distribution. IEEE Transactions on Information Theory, 61(9):5172–5184, 2015.
  7. Logarithmic regret for learning linear quadratic regulators efficiently. In International Conference on Machine Learning, pages 1328–1337. PMLR, 2020.
  8. Kernel change-point detection with auxiliary deep generative models. arXiv preprint arXiv:1901.06077, 2019.
  9. Regret bounds for robust adaptive control of the linear quadratic regulator. Advances in Neural Information Processing Systems, 31, 2018.
  10. Change detection with the kernel cumulative sum algorithm. In 2019 IEEE 58th Conference on Decision and Control (CDC), pages 6092–6099. IEEE, 2019.
  11. Nonparametric bayesian learning of switching linear dynamical systems. Advances in neural information processing systems, 21, 2008.
  12. Online change-point detection of linear regression models. IEEE Transactions on Signal Processing, 67(12):3316–3329, 2019.
  13. Confirmatory bayesian online change point detection in the covariance structure of gaussian processes. arXiv preprint arXiv:1905.13168, 2019.
  14. On deriving the inverse of a sum of matrices. SIAM Review, 23(1):53–60, 1981.
  15. Change-point detection in time-series data based on subspace identification. In Seventh IEEE International Conference on Data Mining (ICDM 2007), pages 559–564. IEEE, 2007.
  16. Tze Leung Lai. Information bounds and quick detection of parameter changes in stochastic systems. IEEE Transactions on Information theory, 44(7):2917–2929, 1998.
  17. Training neural networks for sequential change-point detection. arXiv preprint arXiv:2210.17312, 2022.
  18. M-statistic for kernel change-point detection. Advances in Neural Information Processing Systems, 28, 2015.
  19. State-of-the-art in sequential change-point detection. Methodology and computing in applied probability, 14(3):649–684, 2012.
  20. Albert N Shiryaev. On optimum methods in quickest detection problems. Theory of Probability & Its Applications, 8(1):22–46, 1963.
  21. Analysis and synthesis of switched linear control systems. Automatica, 41(2):181–195, 2005.
  22. Alexander G Tartakovsky. On asymptotic optimality in sequential changepoint detection: Non-iid case. IEEE Transactions on Information Theory, 63(6):3433–3450, 2017.
  23. Efficient computer network anomaly detection by changepoint detection methods. IEEE Journal of Selected Topics in Signal Processing, 7(1):4–11, 2012.
  24. Sequential changepoint detection in neural networks with checkpoints. Statistics and Computing, 32(2):1–19, 2022.
  25. Selective review of offline change point detection methods. Signal Processing, 167:107299, 2020.
  26. Identifying the dynamics of a system by leveraging data from similar systems. In 2022 American Control Conference (ACC), pages 818–824. IEEE, 2022.
  27. Learning dynamical systems by leveraging data from similar systems. arXiv preprint arXiv:2302.04344, 2023.
  28. Linear system theory: the state space approach. Courier Dover Publications, 2008.
  29. Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach. International Journal of Systems Science, 32(8):1055–1061, 2001.
  30. OR Zoeter and TM Heskes. Change point problems in linear dynamical systems. Journal of Machine Learning Research, 6:1999–2026, 2005.
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