PreprintarXiv licencearXiv
Sharp convergence rate of the estimation error of LASSO via the Feature Space Decomposition method
Abstract
In this paper, we use the Feature Space Decomposition (FSD) method to establish an explicit, non-asymptotic, instance-optimal convergence rate for the estimation error of the LASSO in the Gaussian linear regression problem for any signal, any diagonal covariance and any regularization parameter above σξ/√N where σξ is the noise variance and N the number of data.
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BibTeX
@misc{lecue2026sharp,
title = {{Sharp convergence rate of the estimation error of LASSO via the Feature Space Decomposition method}},
author = {Guillaume Lecué and Zong Shang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30622},
eprint = {2610.30622},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30622},
}
RIS
TY - UNPB
TI - Sharp convergence rate of the estimation error of LASSO via the Feature Space Decomposition method
AU - Guillaume Lecué
AU - Zong Shang
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30622
UR - https://arxiv.org/abs/2610.30622
AB - In this paper, we use the Feature Space Decomposition (FSD) method to establish an explicit, non-asymptotic, instance-optimal convergence rate for the estimation error of the LASSO in the Gaussian linear regression problem for any signal, any diagonal covariance and any regularization parameter above σ_ξ/√N where σ_ξ is the noise variance and N the number of data.
ER -