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QUICKEST CHANGE DETECTION WITH APPLICATIONS TO
DISTRIBUTED MULTI-SENSOR SYSTEMS
by
Aleksey S. Polunchenko
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
August 2009
Copyright 2009 Aleksey S. Polunchenko
Object Description
| Title | Quickest change detection with applications to distributed multi-sensor systems |
| Author | Polunchenko, Aleksey S. |
| Author email | polunche@usc.edu; polunchenko@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2009-05-13 |
| Date submitted | 2009 |
| Restricted until | Restricted until 4 Jun. 2011. |
| Date published | 2011-06-04 |
| Advisor (committee chair) |
Mikulevicius, Remigijus Tartakovsky, Alexander |
| Advisor (committee member) |
Goldstein, Larry Medioni, Gerard |
| Abstract | This dissertation is a study of the problem of sequential optimal quickest change-point detection. This problem is addressed in a variety of interrelated contexts, each, in a sense, extending the previous.; The change-point detection problem is concerned with detecting a change in the state of a process available through observations. The sequential setting assumes one makes observations at certain moments of time and, as long as the observations are consistent with the "normal'' state, one is content to let the process continue. If, however, the state changes, then one is interested in detecting that a change has occurred -- preferably as quickly as possible and with as few as possible false detections -- so an appropriate action can be taken.; We first consider the iid setting of this problem, which assumes the observations are independent throughout the entire period of surveillance and such that each observation follows the same known density before change and another also known density after. We focus on the minimax formulation with Pollak's measure of detection delay. In 1985 Pollak introduced the Shiryaev-Roberts-Pollak test, whose detection statistics starts off a random point sampled from the quasi-stationary distribution of the Shiryaev-Roberts statistic, and showed that this procedure possesses a very strong (asymptotic) optimality property. For this and other reasons, since its inception the Shiryaev-Roberts-Pollak test has been considered to be the only candidate for a procedure exactly optimal with respect to Pollak's measure of detection delay. We offer a counterexample showing the Shiryaev-Roberts-Pollak test is not exactly optimal. This is done by proposing a test competitive to the Shiryaev-Roberts-Pollak procedure and performing direct efficiency comparison of the two. The new procedure is a derivative of the Shiryaev-Roberts test, whose detection statistics starts off not zero but a deterministic specially designed point that depends of the false alarm rate. To accentuate the dependence on the starting point, this test is called the Shiryaev-Roberts-r procedure. To perform the comparison we propose a framework for performance evaluation of a broad class of change-point detection procedures that are based on Markov detection statistics. In addition to the Shiryaev-Roberts-Pollak and Shiryaev-Roberts-r procedures the proposed framework covers also such popular procedures as CUSUM and EWMA. The framework consists of a set of integral equations for operating characteristics that are solved numerically.; We study the performance of the Shiryaev-Roberts-r test for different values of the starting point and show that there exists a starting point for which the Shiryaev-Roberts-Pollak test is uniformly worse. This is shown both numerically and analytically, which proves that the Shiryaev-Roberts-Pollak test is not minimax. Also, our numerical techniques allow for computing the quasi-stationary distribution, which is necessary to implement the Shiryaev-Roberts-Pollak test in practice. Finally, using the developed numerical methods we perform a comparative efficiency analysis of the CUSUM, Shiryaev-Roberts-r and Shiryaev-Roberts-Pollak procedures.; Next, we consider the problem of decentralized change-point detection in a distributed multi-sensor setting with quantization, where due to bandwidth constraints the observations are only partially available. Attention is drawn to the case of composite post-change hypotheses where the post-change parameter is unknown. A multi-chart CUSUM-based algorithm capable of handling such situations is proposed. The idea is to use M > 2 putative values of the unknown parameter as "reference'' points, and run M CUSUM tests in parallel, each tuned to the corresponding reference point, and declare a change as soon as either one of the M CUSUM procedures does so. The proposed test is shown to be asymptotically optimal at the reference points, and quite efficient in between. The theoretical results are confirmed by Monte Carlo simulations, which show that even as many as M=2 reference points is enough for a reasonable performance for the entire range of values of the parameter, indicating that the proposed test can be recommended for practical implementation.; Lastly, the developed change-point detection strategies are applied to the area of computer network security. Specifically, the importance and efficiency of change-point detection are demonstrated using the problem of rapid intrusion detection in computer networks as an example. A novel hybrid anomaly-signature intrusion detection system is proposed. The system combines a change-point based anomaly detector with a flow-based spectral signature one. By virtue of extensive performance evaluation accomplished using real-life traffic data, the proposed system is shown to be robust and capable of achieving excellent results in terms of both the detection speed and the frequency of false positives, therefore allowing to detect computer attacks with small detection delays and low false alarm rate. |
| Keyword | sequential analysis; change-point detection; CUSUM; sequential analysis; Shiryaev-Roberts; network security; intrusion detection |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m2282 |
| Rights | Polunchenko, Aleksey S. |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Polunchenko-2949 |
| Archival file | uscthesesreloadpub_Volume44/etd-Polunchenko-2949.pdf |
Description
| Title | Page 1 |
| Full text | QUICKEST CHANGE DETECTION WITH APPLICATIONS TO DISTRIBUTED MULTI-SENSOR SYSTEMS by Aleksey S. Polunchenko A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) August 2009 Copyright 2009 Aleksey S. Polunchenko |
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