Sequential change-point detection: Laplace ...
Document type :
Communication dans un congrès avec actes
Title :
Sequential change-point detection: Laplace concentration of scan statistics and non-asymptotic delay bounds
Author(s) :
Maillard, Odalric Ambrym [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Sequential Learning [SEQUEL]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Sequential Learning [SEQUEL]
Conference title :
Algorithmic Learning Theory
City :
Chicago
Country :
Etats-Unis d'Amérique
Start date of the conference :
2019
Publication date :
2019
HAL domain(s) :
Statistiques [stat]/Autres [stat.ML]
English abstract : [en]
We consider change-point detection in a fully sequential setup, when observations are received one by one and one must raise an alarm as early as possible after any change. We assume that both the change points and the ...
Show more >We consider change-point detection in a fully sequential setup, when observations are received one by one and one must raise an alarm as early as possible after any change. We assume that both the change points and the distributions before and after the change are unknown. We consider the class of piecewise-constant mean processes with sub-Gaussian noise, and we target a detection strategy that is uniformly good on this class (this constrains the false alarm rate and detection delay). We introduce a novel tuning of the GLR test that takes here a simple form involving scan statistics, based on a novel sharp concentration inequality using an extension of the Laplace method for scan-statistics that holds doubly-uniformly in time. This also considerably simplifies the implementation of the test and analysis. We provide (perhaps surprisingly) the first fully non-asymptotic analysis of the detection delay of this test that matches the known existing asymptotic orders, with fully explicit numerical constants. Then, we extend this analysis to allow some changes that are not-detectable by any uniformly-good strategy (the number of observations before and after the change are too small for it to be detected by any such algorithm), and provide the first robust, finite-time analysis of the detection delay.Show less >
Show more >We consider change-point detection in a fully sequential setup, when observations are received one by one and one must raise an alarm as early as possible after any change. We assume that both the change points and the distributions before and after the change are unknown. We consider the class of piecewise-constant mean processes with sub-Gaussian noise, and we target a detection strategy that is uniformly good on this class (this constrains the false alarm rate and detection delay). We introduce a novel tuning of the GLR test that takes here a simple form involving scan statistics, based on a novel sharp concentration inequality using an extension of the Laplace method for scan-statistics that holds doubly-uniformly in time. This also considerably simplifies the implementation of the test and analysis. We provide (perhaps surprisingly) the first fully non-asymptotic analysis of the detection delay of this test that matches the known existing asymptotic orders, with fully explicit numerical constants. Then, we extend this analysis to allow some changes that are not-detectable by any uniformly-good strategy (the number of observations before and after the change are too small for it to be detected by any such algorithm), and provide the first robust, finite-time analysis of the detection delay.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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