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Regularization and Variable Selection Via the Elastic Net
Open accessAbstract
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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“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.”
From Fusion of medical imaging and electronic health records using deep learning: a systematic review and implementation guidelines (2020) · cites this paper as [47]
In the citing paper
“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).”
From A pilot study using frequent inpatient assessments of suicidal thinking to predict short-term postdischarge suicidal behavior (2021) · cites this paper as [29]
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Metadata
- Authors
- Zou, H., & Hastie, T.
- Affiliations
- Stanford University (US)
- Corresponding author
- Hastie, Trevor
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- 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
- 7
- 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
- bronze
- doi.org
- 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 › Computer Science › Signal Processing › 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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