Quickest Change Detection With Post-Change Density Estimation

The problem of quickest change detection in a sequence of independent observations is considered. The pre-change distribution is assumed to be known, while the post-change distribution is unknown. Two tests based on post-change density estimation are developed for this problem, the window-limited no...

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Bibliographic Details
Published in:IEEE transactions on information theory 2024-11, Vol.70 (11), p.8072-8086
Main Authors: Liang, Yuchen, Veeravalli, Venugopal V.
Format: Article
Language:English
Subjects:
(kernel) density estimation
Delays
Density measurement
Estimation
Kernel
Loss measurement
non-parametric statistics
Quickest change detection (QCD)
sequential methods
Training
Vectors
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Summary:The problem of quickest change detection in a sequence of independent observations is considered. The pre-change distribution is assumed to be known, while the post-change distribution is unknown. Two tests based on post-change density estimation are developed for this problem, the window-limited non-parametric generalized likelihood ratio (NGLR) CuSum test and the non-parametric window-limited adaptive (NWLA) CuSum test. Both tests do not assume any knowledge of the post-change distribution, except that the post-change density satisfies certain smoothness conditions that allows for efficient non-parametric estimation; also, they do not require any pre-collected post-change training samples. Under certain convergence conditions on the density estimator, it is shown that both tests are first-order asymptotically optimal, as the false alarm rate goes to zero. The analysis is validated through numerical results, where both tests are compared with baseline tests that have distributional knowledge.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2024.3418379