The DOI matches its Crossref record; 29 of the 29 references it cites were found in a registry or an index.
Piecewise linear regularized solution paths
Open accessAbstract
We consider the generic regularized optimization problem β̂(λ)=arg minβ L(y, Xβ)+λJ(β). Efron, Hastie, Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407–499] have shown that for the LASSO—that is, if L is squared error loss and J(β)=‖β‖1 is the ℓ1 norm of β—the optimal coefficient path is piecewise linear, that is, ∂β̂(λ)/∂λ is piecewise constant. We derive a general characterization of the properties of (loss L, penalty J) pairs which give piecewise linear coefficient paths. Such pairs allow for efficient generation of the full regularized coefficient paths. We investigate the nature of efficient path following algorithms which arise. We use our results to suggest robust versions of the LASSO for regression and classification, and to develop new, efficient algorithms for existing problems in the literature, including Mammen and van de Geer’s locally adaptive regression splines.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
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
The Nature of Statistical Learning Theory
Vapnik, V. N. (1995) · doi:10.1007/978-1-4757-2440-0 · Cited by 39,138
The Elements of Statistical Learning
Hastie, T., Tibshirani, R., & Friedman, J. (2009) · Springer Series in Statistics · doi:10.1007/978-0-387-84858-7 · Cited by 25,970
The Elements of Statistical Learning
Hastie, T., Friedman, J., & Tibshirani, R. (2001) · Springer Series in Statistics · doi:10.1007/978-0-387-21606-5 · Cited by 24,162
Ridge regression: Biased estimation for nonorthogonal problems
Hoerl, A. E., & Kennard, R. W. (1970) · Technometrics · doi:10.1080/00401706.1970.10488634 · Cited by 9,648
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Fan, J., & Li, R. (2001) · Journal of the American Statistical Association · doi:10.1198/016214501753382273 · Cited by 8,900
Robust estimation of a location parameter
Huber, P. J. (1964) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177703732 · Cited by 7,228
Spline Models for Observational Data.
Muller, H.-G., & Wahba, G. (1991) · Journal of the American Statistical Association · doi:10.2307/2290434 · Cited by 4,928
Koenker, R. (2005) · Cambridge University Press eBooks · doi:10.1017/cbo9780511754098 · Cited by 4,551
Cited by
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357
Model Selection and Estimation in Regression with Grouped Variables
Yuan, M., & Lin, Y. (2006) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2005.00532.x · Cited by 7,261
The composite absolute penalties family for grouped and hierarchical variable selection
Zhao, P., Rocha, G., & Yu, B. (2009) · The Annals of Statistics · doi:10.1214/07-aos584 · Cited by 631
Kim, S.-J., Koh, K., Boyd, S., & Gorinevsky, D. (2009) · SIAM Review · doi:10.1137/070690274 · Cited by 615
The solution path of the generalized lasso
Tibshirani, R. J., & Taylor, J. (2011) · The Annals of Statistics · doi:10.1214/11-aos878 · Cited by 553
Metadata
- Authors
- Rosset, S., & Zhu, J.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2007-07-01
- Volume
- 35
- Issue
- 3
- Pages
- 1012-1030
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2057682568
- Cited by
- 481
- References
- 29
- FWCI
- 34.84
- Type
- journal article
- Language
- en
- Open access
- bronze
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Piecewise linear regularized solution paths. https://app.cochat.ai/papers/10.1214/009053606000001370
- The paper
- Rosset, S., & Zhu, J. (2007). Piecewise linear regularized solution paths. The Annals of Statistics. https://doi.org/10.1214/009053606000001370
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
