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Regularization and variable selection via the Elastic Net.

by Hui Zou , Trevor Hastie - J. R. Stat. Soc. Ser. B , 2005
"... Abstract 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, wher ..."
Abstract - Cited by 973 (11 self) - Add to MetaCart
Abstract 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

High dimensional graphs and variable selection with the Lasso

by Nicolai Meinshausen, Peter Bühlmann - ANNALS OF STATISTICS , 2006
"... The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a ..."
Abstract - Cited by 736 (22 self) - Add to MetaCart
The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso

Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties

by Jianqing Fan , Runze Li , 2001
"... Variable selection is fundamental to high-dimensional statistical modeling, including nonparametric regression. Many approaches in use are stepwise selection procedures, which can be computationally expensive and ignore stochastic errors in the variable selection process. In this article, penalized ..."
Abstract - Cited by 948 (62 self) - Add to MetaCart
Variable selection is fundamental to high-dimensional statistical modeling, including nonparametric regression. Many approaches in use are stepwise selection procedures, which can be computationally expensive and ignore stochastic errors in the variable selection process. In this article, penalized

Approaches for Bayesian variable selection

by Edward I. George, Robert E. Mcculloch - Statistica Sinica , 1997
"... Abstract: This paper describes and compares various hierarchical mixture prior formulations of variable selection uncertainty in normal linear regression models. These include the nonconjugate SSVS formulation of George and McCulloch (1993), as well as conjugate formulations which allow for analytic ..."
Abstract - Cited by 234 (5 self) - Add to MetaCart
Abstract: This paper describes and compares various hierarchical mixture prior formulations of variable selection uncertainty in normal linear regression models. These include the nonconjugate SSVS formulation of George and McCulloch (1993), as well as conjugate formulations which allow

An introduction to variable and feature selection

by Isabelle Guyon - Journal of Machine Learning Research , 2003
"... Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available. ..."
Abstract - Cited by 1352 (16 self) - Add to MetaCart
Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available.

Model selection and estimation in regression with grouped variables

by Ming Yuan, Yi Lin , 2006
"... ..."
Abstract - Cited by 1161 (9 self) - Add to MetaCart
Abstract not found

Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools

by Joseph G. Altonji, Todd E. Elder, Christopher R. Taber , 2002
"... In this paper we measure the effect of Catholic high school attendance on educational attainment and test scores. Because we do not have a good instrumental variable for Catholic school attendance, we develop new estimation methods based on the idea that the amount of selection on the observed expla ..."
Abstract - Cited by 538 (14 self) - Add to MetaCart
In this paper we measure the effect of Catholic high school attendance on educational attainment and test scores. Because we do not have a good instrumental variable for Catholic school attendance, we develop new estimation methods based on the idea that the amount of selection on the observed

Calibration and Empirical Bayes Variable Selection

by Edward I. George, I. George, Dean P. Foster - Biometrika , 1997
"... this paper, is that with F =2logp. This choice was proposed by Foster &G eorge (1994) where it was called the Risk Inflation Criterion (RIC) because it asymptotically minimises the maximum predictive risk inflation due to selection when X is orthogonal. This choice and its minimax property were ..."
Abstract - Cited by 192 (20 self) - Add to MetaCart
this paper, is that with F =2logp. This choice was proposed by Foster &G eorge (1994) where it was called the Risk Inflation Criterion (RIC) because it asymptotically minimises the maximum predictive risk inflation due to selection when X is orthogonal. This choice and its minimax property were

Nonparametric regression using Bayesian variable selection

by Michael Smith - Journal of Econometrics , 1996
"... This paper estimates an additive model semiparametrically, while automatically select-ing the significant independent variables and the app~opriatc power transformation of the dependent variable. The nonlinear variables arc modeled as regression splincs, with sig-nificant knots selected fiom a large ..."
Abstract - Cited by 215 (17 self) - Add to MetaCart
This paper estimates an additive model semiparametrically, while automatically select-ing the significant independent variables and the app~opriatc power transformation of the dependent variable. The nonlinear variables arc modeled as regression splincs, with sig-nificant knots selected fiom a

The adaptive LASSO and its oracle properties

by Hui Zou - Journal of the American Statistical Association
"... 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 sc ..."
Abstract - Cited by 683 (10 self) - Add to MetaCart
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
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