519.2 Implementation of the Kullback-Leibler procedure to the change point problem to time series of various nature

Oblakova T. V. (Bauman Moscow State Technical University), Kasupovich E. (Bauman Moscow State Technical University)

STATISTICAL MODELING, MACHINE LEARNING, TIME SERIES, THE PROBLEM OF THE CHANGE POINT DETECTION, THE KLIEP MODEL


doi: 10.18698/2309-3684-2024-4-111127


The paper is devoted to methods to the comparative study of parametric and nonparametric methods for detecting anomaly in time series of various nature. To solve the problem of anomaly detection in series with unknown statistical characteristics, a model based on the estimation of Kulbak-Leibler divergence between distribution laws is considered and implemented. The Kullback-Leibler importance estimation procedure (KLIEP) is applied to calculate the parameters of the linear model. A two-stage algorithm for solving the obtained conditional optimization problem by the gradient descent method was implemented using the original software code, and the cross-validation method was used to evaluate the model's learning ability. A comparative analysis of the quality of fault moment detection by the considered KLIEP method and the classical cumulative sum model (CUSUM) was carried out. When working with simulated data, insignificant variations in such characteristics of KLIEP and CUSUM models as the average time of fault detection and false alarm rate were found. For the real power mode fault detection task, both procedures showed 1-2 false alarms, but KLIEP obtained a narrower time window (5 time intervals vs. 20), which in principle allows much faster and without loss of accuracy anomaly detection. Similar results were obtained when detecting discrepancies in key performance indicators of Internet service. In general, it is shown that the KLIEP model does not degrade the quality of anomaly detection compared to popular models that use statistical characteristics of the series. The advantage of using this approach is demonstrated on real data, since it does not require knowledge of the law of distribution of the time series.


[1] Aminikhanghahi S., Cook D. J. A survey of methods for time series change point detection. Knowledge and information systems, 2017, vol. 51, No. 2, pp. 339-367.
[2] Itoh N., Kurths J. Change-point detection of climate time series by nonparametric method. Proceedings of the world congress on engineering and computer science, 2010, vol. 1, pp. 445-448.
[3] Оblakova Т.V., Каsupovich E. Numerical research of persistent time series based on the ARFIMA model. Маthematical Modeling and Coтputational Methods, 2022, No. 4, pp. 114–125.
[4] Оblakova Т.V., Аlekssev D.S. Comparative analysis of modeling methods and time series forecasting based on the theory of fractal Brownian motion. Маthematical Modeling and Coтputational Methods, 2022, No. 4, pp. 48–62
[5] Shiryaev A. Stohasticheskie zadachi o razladke [Stochastic discorded problems], Litres, 2022, 393 p.
[6] Spivak V. S., Tartakovsky A. G. Bayesian quickest changepoint detection approach to partially observe Markow processes. Proceedings of Moscow Institute of Physics and Technology, 2021, vol. 13, No. 2 (50), pp. 161-170.
[7] Spivak V. Numerical comparison of popular quickest changepoint detection procedures. Proceedings of Moscow Institute of Physics and Technology, 2020, vol. 12, No. 2 (46), pp. 88-98.
[8] Sugiyama M. et al. Direct importance estimation for covariate shift adaptation. Annals of the Institute of Statistical Mathematics, 2008, vol. 60, pp. 699-746.
[9] Kanamori T., Hido S., Sugiyama M. A least-squares approach to direct importance estimation. The Journal of Machine Learning Research, 2009, vol. 10, pp. 1391-1445.
[10] Liu S. et al. Change-point detection in time-series data by relative density-ratio estimation. Neural Networks, 2013, vol. 43, pp. 72-83.
[11] Desobry F., Davy M., Doncarli C. An online kernel change detection algorithm. IEEE Transactions on Signal Processing, 2005, vol. 53, No. 8, pp. 2961-2974.
[12] Chandola V., Vatsavai R. R. A gaussian process based online change detection algorithm for monitoring periodic time series. Proceedings of the Eleventh SIAM International Conference on Data Mining, 2011, pp. 95-106.


Облакова Т.В., Касупович Э. Имплементация процедуры Кульбака-Лейблера к задаче о разладке во временных рядах различной природы. Математическое моделирование и численные методы, 2024, № 4, с. 111–127.



Download article

Количество скачиваний: 272