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DTSTART;TZID=Europe/Paris:20201130T140000
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SUMMARY:Matthieu LERASLE (CNRS-ENSAE-CREST) - "Optimal Change-Point Detection and Localization"
DESCRIPTION:\nThe Statistical Seminar: Every Monday at 2:00 pm.\nTime: 2:00 pm – 3:15 pm\nDate: 30th of November 2020\nPlace: Visio\nMatthieu LERASLE (CNRS-ENSAE-CREST) – “Optimal Change-Point Detection and Localization” \nAbstract: Given a times series Y in R n\, with a piece-wise contant mean and independent components\, the twin problems of change-point detection and change-point localization respectively amount to detecting the existence of times where the mean varies and estimating the positions of those change-points. In this work\, we tightly characterize optimal rates for both problems and uncover the phase transition phenomenon from a global testing problem to a local estimation problem. Introducing a suitable definition of the energy of a change-point\, we first establish in the single change-point setting that the optimal detection threshold is p 2 log log(n). When the energy is just above the detection threshold\, then the problem of localizing the change-point becomes purely parametric: it only depends on the difference in means and not on the position of the change-point anymore. Interestingly\, for most change-point positions\, including all those away from the endpoints of the time series\, it is possible to detect and localize them at a much smaller energy level. In the multiple change-point setting\, we establish the energy detection threshold and show similarly that the optimal localization error of a specific change-point becomes purely parametric. Along the way\, tight optimal rates for Hausdorff and l1 estimation losses of the vector of all change-points positions are also established. Two procedures achieving these optimal rates are introduced. The first one is a least-squares estimator with a new multiscale penalty that favours well spread change-points. The second one is a two-step multiscale post-processing procedure whose computational complexity can be as low as O(n log(n)). Notably\, these two procedures accommodate with the presence of possibly many low-energy and therefore undetectable change-points and are still able to detect and localize high-energy change-points even with the presence of those nuisance parameters. \nOrganizers:\nCristina BUTUCEA (CREST)\, Alexandre TSYBAKOV (CREST)\, Karim LOUNICI (CMAP) \, Zoltan SZABO (CMAP)\nSponsors:\nCREST-CMAP\n \n\n
URL:https://crest.science/event/matthieu-lerasle-2/
CATEGORIES:Statistics
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