Multiple Change-Point Estimation With a Total Variation Penalty

• 成果类型: Article
• 署名作者: Harchaoui, Z.; Levy-Leduc, C.
• 署名单位: Inria; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria; Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2010.tm09181
• 发表日期: 2010
• 页码: 1480-1493
• 关键词: least-squares estimation; regression; approximation; selection; models; Lasso; angle

摘要

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 L-1-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.