The DOI matches its Crossref record; 42 of the 42 references it cites were found in a registry or an index.
Simultaneous Variable Selection
Abstract
We propose a new method for selecting a common subset of explanatory variables where the aim is to model several response variables. The idea is a natural extension of the LASSO technique proposed by Tibshirani (1996) and is based on the (joint) residual sum of squares while constraining the parameter estimates to lie within a suitable polyhedral region. The properties of the resulting convex programming problem are analyzed for the special case of an orthonormal design. For the general case, we develop an efficient interior point algorithm. The method is illustrated on a dataset with infrared spectrometry measurements on 14 qualitatively different but correlated responses using 770 wavelengths. The aim is to select a subset of the wavelengths suitable for use as predictors for as many of the responses as possible.
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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
Model selection and multimodel inference: a practical information-theoretic approach.
Guthery, F. S., Burnham, K. P., & Anderson, D. R. (2003) · The Journal of Wildlife Management · doi:10.2307/3802723 · Cited by 41,495
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
(2005) · Statistics for Biology and Health · doi:10.1007/0-387-27255-0_9 · Cited by 20,133
(2005) · Technometrics · doi:10.1198/tech.2005.s303 · Cited by 17,923
Optimization and Nonsmooth Analysis
Clarke, F. H. (1990) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611971309 · Cited by 10,264
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Fan, J., & Li, R. (2001) · Journal of the American Statistical Association · doi:10.1198/016214501753382273 · Cited by 8,900
Brown, R. A., Hastie, T. J., & Tibshirani, R. J. (1991) · Biometrics · doi:10.2307/2532174 · Cited by 8,176
The adaptive lasso and its oracle properties
Zou, H. (2006) · Journal of the American Statistical Association · doi:10.1198/016214506000000735 · Cited by 7,470
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Bach, F., Jenatton, R., Mairal, J., & Obozinski, G. (2025) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000015 · Cited by 730
Optimization with Sparsity-Inducing Penalties
Bach, F. (2011) · now publishers, Inc. eBooks · doi:10.1561/9781601985118 · Cited by 608
Collaborative Sparse Regression for Hyperspectral Unmixing
Iordache, M.-D., Bioucas-Dias, J. M., & Plaza, A. (2014) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2013.2240001 · Cited by 485
Dimension Reduction and Coefficient Estimation in Multivariate Linear Regression
Yuan, M., Ekici, A., Lu, Z., & Monteiro, R. (2007) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2007.00591.x · Cited by 310
A Unified Framework for High-Dimensional Analysis of $M$-Estimators with Decomposable Regularizers
Negahban, S. N., Ravikumar, P., Wainwright, M. J., & Yu, B. (2012) · Statistical Science · doi:10.1214/12-sts400 · Cited by 287
Metadata
- Authors
- Turlach, B. A., Venables, W. N., & Wright, S. J.
- Venue
- Technometrics
- Publisher
- Informa UK Limited
- Published
- 2005-08
- Volume
- 47
- Issue
- 3
- Pages
- 349-363
- ISSN
- 0040-1706 (ISSN-L)
- 1537-2723
- OpenAlex
- W2045220410
- Cited by
- 386
- References
- 42
- FWCI
- 9.05
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
