Optimal sampling policy for quickest change detection

IEEE Trans. Signal Process.

2021

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We consider the problem of quickest change detection (QCD) in a signal where its observations are obtained using a set of actions, and switching from one action to another comes with a cost. The objective is to design a stopping rule consisting of a sampling policy to determine the sequence of actions used to observe the signal and a stopping time to quickly detect for the change, subject to a constraint on the average observationswitching cost. We propose an open-loop sampling policy of finite window size and a generalized likelihood ratio (GLR) Cumulative Sum (CuSum) stopping time for the QCD problem. We show that the GLR CuSum stopping time is asymptotically optimal with a properly designed sampling policy and formulate the design of this sampling policy as a quadratic programming problem. We prove that it is sufficient to consider policies of window size not more than one when designing policies of finite window size and propose several algorithms that solve this optimization problem with theoretical guarantees. Finally, we apply our approach to the problem of QCD of a partially observed graph signal and empirically demonstrate the performance of our proposed stopping times.

Section: A Related Workmentioning

confidence: 99%

Asymptotically Optimal Sampling Policy for Quickest Change Detection With Observation-Switching Cost

IEEE Trans. Signal Process.

2021

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“…Following Theorem 6.16 in [29], this upper bound then yields a lower bound for the ARL of τ W-SGLR (b) in Theorem 3. (25). For any ν n ∈N∪{∞}, we have…”

Section: B Conditions For Asymptotic Optimalitymentioning

confidence: 99%

Quickest Change Detection in the Presence of a Nuisance Change

IEEE Trans. Signal Process.

2019

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In the quickest change detection problem in which both nuisance and critical changes may occur, the objective is to detect the critical change as quickly as possible without raising an alarm when either there is no change or a nuisance change has occurred. A window-limited sequential change detection procedure based on the generalized likelihood ratio test statistic is proposed. A recursive update scheme for the proposed test statistic is developed and is shown to be asymptotically optimal under mild technical conditions. In the scenario where the post-change distribution belongs to a parametrized family, a generalized stopping time and a lower bound on its average run length are derived. The proposed stopping rule is compared with the finite moving average (FMA) stopping time and the naive 2-stage procedure that detects the nuisance or critical change using separate CuSum stopping procedures for the nuisance and critical changes. Simulations demonstrate that the proposed rule outperforms the FMA stopping time and the 2-stage procedure, and experiments on a real dataset on bearing failure verify the performance of the proposed stopping time. Index TermsQuickest change detection, nuisance change, Generalized Likelihood Ratio Test (GLRT), average run length, average detection delay under a nuisance change, and propose a window-limited stopping time that ignores the nuisance change but detects the critical change as quickly as possible. A. Related WorkExisting works in QCD that consider the problem where observations are not generated i.i.d. before and after the change-point can be categorized into three main categories. In the first category, the papers [31]-[33] consider the problem where the pre-change distribution and the post-change distribution are modeled as hidden Markov models (HMMs). In [31], the authors proved the asymptotic optimality of the CuSum procedure for the HMM signal model in the sense of Lorden. In [32], the authors developed the Shiryayev-Roberts-Pollak (SRP) rule for the HMM signal model and proved its optimality in the sense of Pollak. The authors of [33] consider the problem where the vector parameter of a two-state HMM changes at some unknown time. The second category of papers [34], [35] considers a QCD problem which relaxes the i.i.d. assumption. In [34], the authors established the optimality of CuSum and the Shiryayev-Roberts stopping rule in the class of random processes with likelihood ratios that satisfy certain independence and stationary conditions. The class of random processes includes Markov chains, AR processes, and processes evolving on a circle. In [35], the authors considered the Bayesian QCD problem where conditions on the asymptotic behavior of the likelihood process are assumed. Unlike all the aforementioned papers, the signal model in our QCD problem with nuisance change cannot be modeled by an HMM, and the likelihood ratios generated by our signal model are non-stationary. In the third category, the papers [36]-[41] consider QCD of transient changes, where the change i...

“…For the case where the post-change distribution is unknown, Lorden [20] showed that the Generalized Likelihood Ratio CuSum is asymptotically optimal for the case of finite multiple post-change distributions. Other methods were also proposed for the case when the post-change distribution is unknown to a certain degree [22,[24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Quickest Change Detection Under a Nuisance Change

2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

2018

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We consider the problem of quickest change detection (QCD) for a signal which may undergo both a nuisance and a critical change. Our goal is to detect the critical change without raising a false alarm over the nuisance change. An optimal sequential change detection procedure is proposed for the Bayesian formulation of our QCD problem. A sequential change detection procedure based on the generalized likelihood ratio test (GLRT) statistic is also proposed for the non-Bayesian formulation. We show that our proposed test statistics can be computed efficiently via respective recursive update schemes. We compare our proposed stopping rules with the naive 2-stage procedures, which attempt to detect the changes using separate optimal stopping procedures (i.e., the Shiryaev procedure in the Bayesian formulation, and the CuSum procedure in the non-Bayesian formulation) for the nuisance and critical changes. Simulations demonstrate that our proposed rules outperform the 2-stage procedures.