The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
On the LASSO and its Dual
Abstract
Proposed by Tibshirani, the least absolute shrinkage and selection operator (LASSO) estimates a vector of regression coefficients by minimizing the residual sum of squares subject to a constraint on the l 1-norm of the coefficient vector. The LASSO estimator typically has one or more zero elements and thus shares characteristics of both shrinkage estimation and variable selection. In this article we treat the LASSO as a convex programming problem and derive its dual. Consideration of the primal and dual problems together leads to important new insights into the characteristics of the LASSO estimator and to an improved method for estimating its covariance matrix. Using these results we also develop an efficient algorithm for computing LASSO estimates which is usable even in cases where the number of regressors exceeds the number of observations. An S-Plus library based on this algorithm is available from StatLib.
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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
Linear Statistical Inference and its Applications: Second Editon
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Atomic Decomposition by Basis Pursuit
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Atomic Decomposition by Basis Pursuit
Chen, S. S., Donoho, D. L., & Saunders, M. A. (2001) · SIAM Review · doi:10.1137/s003614450037906x · Cited by 5,085
A Statistical View of Some Chemometrics Regression Tools
Frank, L. E., & Friedman, J. H. (1993) · Technometrics · doi:10.1080/00401706.1993.10485033 · Cited by 2,213
Subset Selection in Regression
(2003) · Technometrics · doi:10.1198/tech.2003.s144 · Cited by 1,463
Penalized Regressions: The Bridge versus the Lasso
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A new approach to variable selection in least squares problems
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Self-citation
Cited by
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357
High-dimensional graphs and variable selection with the Lasso
Meinshausen, N., & Bühlmann, P. (2006) · The Annals of Statistics · doi:10.1214/009053606000000281 · Cited by 2,521
Variable selection in regression—a tutorial
Andersen, C. M., & Bro, R. (2010) · Journal of Chemometrics · doi:10.1002/cem.1360 · Cited by 697
Optimization with Sparsity-Inducing Penalties
Bach, F. (2011) · now publishers, Inc. eBooks · doi:10.1561/9781601985118 · Cited by 608
Penalized regression, standard errors, and Bayesian lassos
Casella, G., Ghosh, M., Gill, J., & Kyung, M. (2010) · Bayesian Analysis · doi:10.1214/10-ba607 · Cited by 567
Metadata
- Authors
- Osborne, M. R., Presnell, B., & Turlach, B. A.
- Venue
- Journal of Computational and Graphical Statistics
- Publisher
- Informa UK Limited
- Published
- 2000-06
- Volume
- 9
- Issue
- 2
- Pages
- 319-337
- ISSN
- 1061-8600 (ISSN-L)
- 1537-2715
- OpenAlex
- W1984568490
- Cited by
- 696
- References
- 19
- FWCI
- 7.13
- Type
- journal article
- Language
- en
- Open access
- closed
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- Osborne, M. R., Presnell, B., & Turlach, B. A. (2000). On the LASSO and its Dual. Journal of Computational and Graphical Statistics. https://doi.org/10.1080/10618600.2000.10474883
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