Quickest Change Detection With Non-Stationary Post-Change Observations

Yuchen Liang, Alexander G. Tartakovsky, Venugopal V. Veeravalli

Research output: Contribution to journalArticlepeer-review

Abstract

The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. The pre-change observations are assumed to be stationary with a known distribution, while the post-change observations are allowed to be non-stationary with some possible parametric uncertainty in their distributions. In particular, it is assumed that the cumulative Kullback-Leibler divergence between the post-change and the pre-change distributions grows in a certain manner 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 Cumulative Sum (CuSum) procedure is developed, and shown to achieve the lower bound asymptotically. For the case where the post-change distributions have parametric uncertainty, a window-limited (WL) generalized likelihood-ratio (GLR) CuSum procedure is developed and is shown to achieve the universal lower bound asymptotically. Extensions to the case with dependent observations are discussed. The analysis is validated through numerical results on synthetic data. The use of the WL-GLR-CuSum procedure in monitoring pandemics is also demonstrated.

Original languageEnglish (US)
Pages (from-to)3400-3414
Number of pages15
JournalIEEE Transactions on Information Theory
Volume69
Issue number5
DOIs
StatePublished - May 1 2023
Externally publishedYes

Keywords

  • CuSum procedure
  • Quickest change detection
  • generalized likelihood-ratio CuSum procedure
  • non-stationary observations
  • pandemic monitoring

ASJC Scopus subject areas

  • Information Systems
  • Library and Information Sciences
  • Computer Science Applications

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