Sequential changepoint detection: Laplace concentration of scan statistics and nonasymptotic delay bounds
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Proceedings of the 30th International Conference on Algorithmic Learning Theory, PMLR 98:610632, 2019.
Abstract
We consider changepoint 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 piecewiseconstant mean processes with subGaussian 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 scanstatistics
that holds doublyuniformly in time. This also considerably simplifies the implementation of the test and analysis.
We provide (perhaps surprisingly) the first fully nonasymptotic 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 notdetectable by any uniformlygood 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, finitetime analysis of the detection delay.
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