Titre :

Sequential change-point detection: Laplace concentration of scan statistics and non-asymptotic delay bounds

Auteur(s) :

Maillard, Odalric Ambrym [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Sequential Learning [SEQUEL]

Titre de la manifestation scientifique :

Algorithmic Learning Theory

Ville :

Chicago

Pays :

Etats-Unis d'Amérique

Date de début de la manifestation scientifique :

2019

Date de publication :

2019

Discipline(s) HAL :

Statistiques [stat]/Autres [stat.ML]

Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

BANDITS MANCHOTS POUR SIGNAUX NON-STATIONNAIRES ET STRUCTURES

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL