The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
A new approach to variable selection in least squares problems
Abstract
The title Lasso has been suggested by Tibshirani (1996) as a colourful name for a technique of variable selection which requires the minimization of a sum of squares subject to an l1 bound κ on the solution. This forces zero components in the minimizing solution for small values of κ. Thus this bound can function as a selection parameter. This paper makes two contributions to computational problems associated with implementing the Lasso: (1) a compact descent method for solving the constrained problem for a particular value of κ is formulated, and (2) a homotopy method, in which the constraint bound κ becomes the homotopy parameter, is developed to completely describe the possible selection regimes. Both algorithms have a finite termination property. It is suggested that modified Gram-Schmidt orthogonalization applied to an augmented design matrix provides an effective basis for implementing the algorithms.
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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
Cited by
Regularization and Variable Selection Via the Elastic Net
Zou, H., & Hastie, T. (2005) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2005.00503.x · Cited by 20,957
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357
Sparse Principal Component Analysis
Zou, H., Hastie, T., & Tibshirani, R. (2006) · Journal of Computational and Graphical Statistics · doi:10.1198/106186006x113430 · Cited by 3,152
A significance test for the lasso
Lockhart, R., Taylor, J., Tibshirani, R. J., & Tibshirani, R. (2014) · The Annals of Statistics · doi:10.1214/13-aos1175 · Cited by 541
An Equivalence between the Lasso and Support Vector Machines
Jaggi, M. (2013) · arXiv · doi:10.48550/arxiv.1303.1152 · Cited by 35
“Since naive grid-search for the best parameter is error-prone and comes without guarantees between the grid-values, algorithms that follow the solution path — as the regularization parameter changes — have been developed for both SVMs [19] and Lasso [31, 10], and have become popular in particular on the Lasso side.”
Method
Metadata
- Authors
- Osborne, M.
- Venue
- IMA Journal of Numerical Analysis
- Publisher
- Oxford University Press (OUP)
- Published
- 2000-07-01
- Volume
- 20
- Issue
- 3
- Pages
- 389-403
- ISSN
- 0272-4979 (ISSN-L)
- 1464-3642
- OpenAlex
- W2062102668
- Cited by
- 859
- References
- 1
- FWCI
- 3.00
- Type
- journal article
- Language
- en
- Open access
- closed
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