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The Adaptive Lasso and Its Oracle Properties
Abstract
The lasso is a popular technique for simultaneous estimation and variable selection. Lasso variable selection has been shown to be consistent under certain conditions. In this work we derive a necessary condition for the lasso variable selection to be consistent. Consequently, there exist certain scenarios where the lasso is inconsistent for variable selection. We then propose a new version of the lasso, called the adaptive lasso, where adaptive weights are used for penalizing different coefficients in the ℓ1 penalty. We show that the adaptive lasso enjoys the oracle properties; namely, it performs as well as if the true underlying model were given in advance. Similar to the lasso, the adaptive lasso is shown to be near-minimax optimal. Furthermore, the adaptive lasso can be solved by the same efficient algorithm for solving the lasso. We also discuss the extension of the adaptive lasso in generalized linear models and show that the oracle properties still hold under mild regularity conditions. As a byproduct of our theory, the nonnegative garotte is shown to be consistent for variable selection.
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“Similarly, multivariate LASSO models (Zou, 2006;Nicolai and Bühlmann Peter, 2010;Mankoo et al., 2011) have been investigated.”
From Using machine learning approaches for multi-omics data analysis: A review (2021) · cites this paper as Zou, 2006
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Metadata
- Authors
- Zou, H.
- Affiliations
- University of Minnesota (US)
- Corresponding author
- Zou, Hui
- ORCID
- Zou, Hui
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2006-12-01
- Volume
- 101
- Issue
- 476
- Pages
- 1418-1429
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2020925091
- Cited by
- 7,470
- References
- 23
- Citations by year
- 2026: 324 · 2025: 476 · 2024: 474 · 2023: 454 · 2022: 567 · 2021: 639 · 2020: 528 · 2019: 548 · 2018: 473 · 2017: 443 · 2016: 416 · 2015: 388 · 2014: 385 · 2013: 361 · 2012: 304
- FWCI
- 76.03
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- 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
- adaptive LASSO, LASSO, feature selection, oracle property, consistency, adaptive weighting, l1 penalty, generalized linear models
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