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arXiv · 2311.15128

Quickest Change Detection with Post-Change Density Estimation

Yuchen Liang·Venugopal V. Veeravalli
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Abstract

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.

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Yuchen Liang, Venugopal V. Veeravalli. 2023-11-25. Quickest Change Detection with Post-Change Density Estimation. https://arxiv.org/abs/2311.15128

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