Least angle regression
Open accessAbstract
The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to select a parsimonious set for the efficient prediction of a response variable. Least Angle Regression (LARS), a new model selection algorithm, is a useful and less greedy version of traditional forward selection methods. Three main properties are derived: (1) A simple modification of the LARS algorithm implements the Lasso, an attractive version of ordinary least squares that constrains the sum of the absolute regression coefficients; the LARS modification calculates all possible Lasso estimates for a given problem, using an order of magnitude less computer time than previous methods. (2) A different LARS modification efficiently implements Forward Stagewise linear regression, another promising new model selection method; this connection explains the similar numerical results previously observed for the Lasso and Stagewise, and helps us understand the properties of both methods, which are seen as constrained versions of the simpler LARS algorithm. (3) A simple approximation for the degrees of freedom of a LARS estimate is available, from which we derive a Cp estimate of prediction error; this allows a principled choice among the range of possible LARS estimates. LARS and its variants are computationally efficient: the paper describes a publicly available algorithm that requires only the same order of magnitude of computational effort as ordinary least squares applied to the full set of covariates.
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Unlike stepwise variable selection procedures, LARS does not over-inflate effect size estimates during variable selection nor bias hypothesis tests of those effect sizes.
“Unlike stepwise variable selection procedures, LARS does not over-inflate effect size estimates during variable selection,14 nor bias hypothesis tests of those effect sizes.19”
From A structured approach to hypotheses involving continuous exposures over the life course (2016) · cites this paper as [14]
The structured approach for binary exposures is based on least angle regression (LARS).
“We developed a structured approach for binary exposures,13 based on least angle regression (LARS),14 that demonstrated more accuracy in simulation than other methods.”
From A structured approach to hypotheses involving continuous exposures over the life course (2016) · cites this paper as [14]
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- Authors
- Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R.
- Affiliations
- Stanford University (US)
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2004-04-01
- Volume
- 32
- Issue
- 2
- Pages
- 407-499
- ISSN
- 0090-5364 (ISSN-L)
- 2168-8966
- OpenAlex
- W2063978378
- Cited by
- 9,357
- References
- 57
- Citations by year
- 2026: 145 · 2025: 242 · 2024: 306 · 2023: 355 · 2022: 424 · 2021: 611 · 2020: 542 · 2019: 601 · 2018: 588 · 2017: 566 · 2016: 565 · 2015: 665 · 2014: 630 · 2013: 585 · 2012: 599
- FWCI
- 126.61
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Statistics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (9971405, 0072360, 0072661)
- National Institutes of Health
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- least angle regression, LARS, LASSO, model selection, feature selection, forward selection, backward elimination, degrees of freedom, constrained regression, computational efficiency
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 ›
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