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Multiple Change-Point Estimation With a Total Variation Penalty

Zaid Harchaoui 1 Céline Lévy-Leduc 2
1 LEAR - Learning and recognition in vision
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : We propose a new approach for dealing with the estimation of the location of change-points in one-dimensional piecewise constant signals observed in white noise. Our approach consists in reframing this task in a variable selection context. We use a penalized least-square criterion with a ℓ1-type penalty for this purpose. We explain how to implement this method in practice by using the LARS / LASSO algorithm. We then prove that, in an appropriate asymptotic framework, this method provides consistent estimators of the change points with an almost optimal rate. We finally provide an improved practical version of this method by combining it with a reduced version of the dynamic programming algorithm and we successfully compare it with classical methods.
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Submitted on : Thursday, January 2, 2014 - 9:39:56 PM
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Zaid Harchaoui, Céline Lévy-Leduc. Multiple Change-Point Estimation With a Total Variation Penalty. Journal of the American Statistical Association, Taylor & Francis, 2010, 105 (492), pp.1480-1493. ⟨10.1198/jasa.2010.tm09181⟩. ⟨hal-00923474⟩



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