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Multiple Change-Point Estimation With a Total Variation Penalty
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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Cites
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
Cited by
Optimal Detection of Changepoints With a Linear Computational Cost
Killick, R., Fearnhead, P., & Eckley, I. A. (2012) · Journal of the American Statistical Association · doi:10.1080/01621459.2012.737745 · Cited by 2,548
TVSum: Summarizing web videos using titles
Song, Y., Vallmitjana, J., Stent, A., & Jaimes, A. (2015) · 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2015.7299154 · Cited by 623
Wild binary segmentation for multiple change-point detection
Fryzlewicz, P. (2014) · The Annals of Statistics · doi:10.1214/14-aos1245 · Cited by 566
Identifying Latent Structures in Panel Data
Su, L., Shi, Z., & Phillips, P. C. B. (2016) · Econometrica · doi:10.3982/ecta12560 · Cited by 265
Metadata
- Authors
- Harchaoui, Z., & Lévy-Leduc, C.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2010-12-01
- Volume
- 105
- Issue
- 492
- Pages
- 1480-1493
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2118673550
- Cited by
- 311
- References
- 1
- FWCI
- 5.39
- Type
- journal article
- Language
- en
- Open access
- closed
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