Abstract
This paper devises new hypothesis tests for detecting changes in the scale of interdependent and serially correlated data streams, i.e, proportional changes of the mean and (co-)variance. Such procedures are of great importance in various networking contexts, since they enable automatic detection of changes, e.g. in the network load. Assuming the underlying structure is Gaussian, we compute the log-likelihood ratio test statistic, either as a function of the observations themselves or as a function of the innovations (i.e., a sequence of i.i.d. Gaussians, to be extracted from the observations). An alarm is raised if the test statistic exceeds a certain threshold. Based on large deviations techniques, we demonstrate how the threshold is chosen such that the ratio of false alarms is kept at a predefined (low) level. Numerical experiments validate the procedure, and demonstrate the merits of a multidimensional detection approach (over multiple one-dimensional tests). Also a detailed comparison between the observations-based approach and the innovations-based approach is provided.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Addie, R., Mannersalo, P., Norros, I.: Most probable paths and performance formulae for buffers with Gaussian input traffic. European Transactions on Telecommunications 13, 183–196 (2002)
Basseville, M., Nikiforov, I.: Detection of Abrupt Changes: Theory and Application, vol. 104. Prentice Hall, Englewood Cliffs, NJ, USA (1993)
Brockwell, P., Davis, R.: Time Series: Theory and Methods. Springer, Berlin (1987)
Brodsky, B.E., Darkhovsky, B.S.: Nonparametric Methods in Change-Point Problems. Kluwer Academic Publishers, The Netherlands (1993)
Bucklew, J.: Large Deviation Techniques in Decision, Simulation, and Estimation. Wiley Series in Probability and Mathematical Statistics. Wiley, New York (1990)
Callegari, C., Coluccia, A., D’Alconzo, A., Ellens, W., Giordano, S., Mandjes, M., Pagano, M., Pepe, T., Ricciato, F., Żuraniewski, P.: A methodological overview on anomaly detection. In: Biersack, E., Callegari, C., Matijasevic, M. (eds.) Data Traffic Monitoring and Analysis, pp. 148–183. Springer, Berlin (2013)
Casella, G., Berger, R.L.: Statistical Inference, vol. 70. Duxbury Press, Belmont (1990)
Chen, J., Gupta, A.: Parametric Statistical Change Point Analysis: With Applications to Genetics, Medicine, and Finance. Springer, Berlin (2012)
Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications, 2nd edn. Springer, New York (1998)
Deshayes, J., Picard, D.: Off-line statistical analysis of change-point models using non parametric and likelihood methods. In: Basseville, M., Benveniste, A. (eds.) Detection of Abrupt Changes in Signals and Dynamical Systems. LNCS, vol. 77, pp. 103–168. Springer, Heidelberg (1986)
Ellens, W., Kuhn, J., Mandjes, M., Żuraniewski, P.: Changepoint detection for dependent Gaussian sequences. arXiv:1307.0938 (2013) (submitted)
Mandjes, M.: Large Deviations for Gaussian Queues. John Wiley & Sons, Chichester (2007)
Mandjes, M., Żuraniewski, P.: M/G/∞ transience, and its applications to overload detection. Performance Evaluation, 507–527 (2011)
Page, E.: Continuous inspection scheme. Biometrika 41, 100–115 (1954)
Robbins, M., Gallagher, C., Lund, R., Aue, A.: Mean shift testing in correlated data. Journal of Time Series Analysis 32, 498–511 (2011)
Siegmund, D.: Sequential Analysis. Springer, New York (1985)
Sperotto, A., Mandjes, M., Sadre, R., de Boer, P.T., Pras, A.: Autonomic parameter tuning of anomaly-based IDSs: An SSH case study. IEEE Transactions on Network and Service Management 9, 128–141 (2012)
Tartakovsky, A.G., Rozovskii, B.L., Blazek, R.B., Kim, H.: A novel approach to detection of intrusions in computer networks via adaptive sequential and batch-sequential change-point detection methods. IEEE Transactions on Signal Processing 54, 3372–3382 (2006)
Tartakovsky, A.G., Veeravalli, V.: Change-point detection in multichannel and distributed systems. In: Mukhopadhyay, N., Datta, S., Chattopadhyay, S. (eds.) Applied Sequential Methodologies: Real-World Examples with Data Analysis, pp. 339–370. Marcel Dekker, NY (2004)
Wilson, M. (2006), A historical view of network traffic models. Unpublished survey paper, http://www.arl.wustl.edu/~mlw2/classpubs/traffic_models/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Kuhn, J., Ellens, W., Mandjes, M. (2014). Detecting Changes in the Scale of Dependent Gaussian Processes: A Large Deviations Approach. In: Sericola, B., Telek, M., Horváth, G. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2014. Lecture Notes in Computer Science, vol 8499. Springer, Cham. https://doi.org/10.1007/978-3-319-08219-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-08219-6_12
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08218-9
Online ISBN: 978-3-319-08219-6
eBook Packages: Computer ScienceComputer Science (R0)