A kernel multiple change-point algorithm via model selection

Sylvain Arlot 1, 2 Alain Celisse 3, 4 Zaid Harchaoui 5
2 SELECT - Model selection in statistical learning
Inria Saclay - Ile de France, LMO - Laboratoire de Mathématiques d'Orsay, CNRS - Centre National de la Recherche Scientifique : UMR
3 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe, CERIM - Santé publique : épidémiologie et qualité des soins-EA 2694, Polytech Lille, Université de Lille 1, IUT’A
Abstract : We tackle the change-point problem with data belonging to a general set. We build a penalty for choosing the number of change-points in the kernel-based method of Harchaoui and Cappé (2007). This penalty generalizes the one proposed by Lebarbier (2005) for one-dimensional signals. We prove a non-asymptotic oracle inequality for the proposed method, thanks to a new concentration result for some function of Hilbert-space valued random variables. Experiments on synthetic data illustrate the accuracy of our method, showing that it can detect changes in the whole distribution of data, even when the mean and variance are constant.
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Submitted on : Friday, March 18, 2016 - 4:10:33 PM
Last modification on : Saturday, February 18, 2017 - 1:14:36 AM
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  • HAL Id : hal-00671174, version 2
  • ARXIV : 1202.3878

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Sylvain Arlot, Alain Celisse, Zaid Harchaoui. A kernel multiple change-point algorithm via model selection. 2016. <hal-00671174v2>

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