TY - GEN
T1 - QUICKEST DETECTION OF COMPOSITE AND NON-STATIONARY CHANGES WITH APPLICATION TO PANDEMIC MONITORING
AU - Liang, Yuchen
AU - Veeravalli, Venugopal V.
N1 - Funding Information:
This work was supported in part by the National Science Foundation under grant ECCS-2033900, and by the Army Research Laboratory under Co-operative Agreement W911NF-17-2-0196, through the University of Illinois at Urbana-Champaign.
Publisher Copyright:
© 2022 IEEE
PY - 2022
Y1 - 2022
N2 - The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. The pre-change distribution is assumed to be known and stationary, while the post-change distributions are assumed to evolve in a pre-determined non-stationary manner with some possible parametric uncertainty. In particular, it is assumed that the cumulative KL divergence between the post-change and the pre-change distributions grows super-linearly with time after the change-point. For the case where the post-change distributions are known, a universal asymptotic lower bound on the delay is derived, as the false alarm rate goes to zero. Furthermore, a window-limited CuSum test is developed, and shown to be asymptotically optimal. For the case where the post-change distributions have parametric uncertainty, a window-limited generalized likelihood-ratio test is developed and is shown to be asymptotically optimal. The analysis is validated through numerical results on synthetic data. The use of the window-limited generalized likelihood-ratio test in monitoring pandemics is also demonstrated.
AB - The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. The pre-change distribution is assumed to be known and stationary, while the post-change distributions are assumed to evolve in a pre-determined non-stationary manner with some possible parametric uncertainty. In particular, it is assumed that the cumulative KL divergence between the post-change and the pre-change distributions grows super-linearly with time after the change-point. For the case where the post-change distributions are known, a universal asymptotic lower bound on the delay is derived, as the false alarm rate goes to zero. Furthermore, a window-limited CuSum test is developed, and shown to be asymptotically optimal. For the case where the post-change distributions have parametric uncertainty, a window-limited generalized likelihood-ratio test is developed and is shown to be asymptotically optimal. The analysis is validated through numerical results on synthetic data. The use of the window-limited generalized likelihood-ratio test in monitoring pandemics is also demonstrated.
KW - generalized likelihood-ratio (GLR) test
KW - non-stationary observations
KW - pandemic monitoring
KW - Quickest change detection (QCD)
KW - window-limited sequential test
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U2 - 10.1109/ICASSP43922.2022.9747602
DO - 10.1109/ICASSP43922.2022.9747602
M3 - Conference contribution
AN - SCOPUS:85131226974
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 5807
EP - 5811
BT - 2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 47th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022
Y2 - 23 May 2022 through 27 May 2022
ER -