Cited by 20,957Statistical Methods and InferenceAdvanced Statistical Methods and ModelsSparse and Compressive Sensing Techniques

Regularization and Variable Selection Via the Elastic Net

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Zou, Hui, Hastie, Trevor·2005·Journal of the Royal Statistical Society Series B: Statistical Methodology

Abstract

Summary: We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in or out of the model together. The elastic net is particularly useful when the number of predictors (p) is much bigger than the number of observations (n). By contrast, the lasso is not a very satisfactory variable selection method in the p≫n case. An algorithm called LARS-EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lasso.

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Crossref · 10.1111/j.1467-9868.2005.00503.x

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  • When there are disproportionately few samples relative to the number of features, or when some input features are sparsely represented, early or late fusion is preferred because they can be implemented with traditional machine learning algorithms better suited to such data.

    “For example, if there are disproportionately few samples relative to the number of features in the dataset or if some of the input features are sparsely represented, early or late fusion is preferred because they can be implemented with traditional machine learning algorithms (e.g., Lasso and ElasticNet47) that are better suited for this type of data48.”
  • The elastic net algorithm was used because penalization improves prediction accuracy and maintains clinical interpretability compared with less transparent machine learning algorithms.

    “We used the elastic net algorithm, given substantial evidence that penalization improves prediction accuracy,25–27 alongside its well-established accuracy and robustness28,29 and ability to maintain clinical interpretability compared with less transparent machine learning algorithms (eg, random forests, neural networks).”

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Authors
Zou, H., & Hastie, T.
Affiliations
Stanford University (US)
Corresponding author
Hastie, Trevor
Venue
Journal of the Royal Statistical Society Series B: Statistical Methodology
Published
2005-03-09
Volume
67
Issue
2
Pages
301-320
ISSN
  • 1369-7412 (ISSN-L)
  • 1467-9868
OpenAlex
W2122825543
Cited by
20,957
References
5
Citations by year
2026: 1933 · 2025: 1906 · 2024: 1653 · 2023: 1540 · 2022: 1664 · 2021: 1924 · 2020: 1702 · 2019: 1536 · 2018: 1338 · 2017: 1092 · 2016: 949 · 2015: 884 · 2014: 727 · 2013: 585 · 2012: 468
FWCI
79.40
Type
journal article
Language
en
Open access
Locations
  • Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
Funders
  • National Science Foundation (DMS-0204162)
  • National Institutes of Health (RO1-EB0011988-08)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
  • Physical Sciences › Engineering › Computational Mechanics › Sparse and Compressive Sensing Techniques
Keywords
elastic net, regularization, feature selection, LASSO, high-dimensional data, correlated predictors, grouping effect, regularization path, sparse representation

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