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Denoising and change point localisation in piecewise-constant high-dimensional regression coefficients
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Wang, Fan, Madrid, Oscar, Yu, Yi and Rinaldo, Alessandro (2022) Denoising and change point localisation in piecewise-constant high-dimensional regression coefficients. In: 25th International Conference on Artificial Intelligence and Statistics, Virtual conference, 28-30 Mar 2022. Published in: Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, 151 pp. 4309-4338.
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WRAP-Denoising-change-point-localisation-piecewise-constant-high-dimensional-regression-coefficients-22.pdf - Accepted Version - Requires a PDF viewer. Download (684Kb) | Preview |
Official URL: https://proceedings.mlr.press/v151/wang22c.html
Abstract
We study the theoretical properties of the fused lasso procedure originally proposed by Tibshirani et al. (2005) in the context of a linear regression model in which the regression coefficient are totally ordered and assumed to be sparse and piecewise constant. Despite its popularity, to the best of our knowledge, estimation error bounds in high-dimensional settings have only been obtained for the simple case in which the design matrix is the identity matrix. We formulate a novel restricted isometry condition on the design matrix that is tailored to the fused lasso estimator and derive estimation bounds for both the constrained version of the fused lasso assuming dense coefficients and for its penalised version. We observe that the estimation error can be dominated by either the lasso or the fused lasso rate, depending on whether the number of non-zero coefficient is larger than the number of piece-wise constant segments. Finally, we devise a post-processing procedure to recover the piecewise-constant pattern of the coefficients. Extensive numerical experiments support our theoretical findings.
| Item Type: | Conference Item (Paper) | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
| Library of Congress Subject Headings (LCSH): | Regression analysis -- Mathematical models, Piecewise linear topology | |||||||||
| Series Name: | Proceedings of Machine Learning Research | |||||||||
| Journal or Publication Title: | Proceedings of The 25th International Conference on Artificial Intelligence and Statistics | |||||||||
| Publisher: | PMLR | |||||||||
| Official Date: | 2022 | |||||||||
| Dates: |
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| Volume: | 151 | |||||||||
| Page Range: | pp. 4309-4338 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Copyright Holders: | Copyright 2022 by the author(s). | |||||||||
| Date of first compliant deposit: | 6 September 2022 | |||||||||
| Date of first compliant Open Access: | 6 September 2022 | |||||||||
| RIOXX Funder/Project Grant: |
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| Conference Paper Type: | Paper | |||||||||
| Title of Event: | 25th International Conference on Artificial Intelligence and Statistics | |||||||||
| Type of Event: | Conference | |||||||||
| Location of Event: | Virtual conference | |||||||||
| Date(s) of Event: | 28-30 Mar 2022 |
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