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113
Rate Minimaxity of the Lasso and Dantzig Selector for the ℓq Loss in ℓr Balls
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2010
"... We consider the estimation of regression coefficients in a highdimensional linear model. For regression coefficients in ℓr balls, we provide lower bounds for the minimax ℓq risk and minimax quantiles of the ℓq loss for all design matrices. Under an ℓ0 sparsity condition on a target coefficient vect ..."
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Cited by 24 (5 self)
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vector, we sharpen and unify existing oracle inequalities for the Lasso and Dantzig selector. We derive oracle inequalities for target coefficient vectors with many small elements and smaller threshold levels than the universal threshold. These oracle inequalities provide sufficient conditions
LASSO AND DANTZIG SELECTORS FOR NONPARAMETRIC AND HIGHDIMENSIONAL REGRESSION
"... Yi = g(Zi) + Wi, i = 1,..., n, where we wish to estimate the function g given the data under the assumption that the Wi are independent indentically distributed Gaussian error terms and g lies inside of some function space ..."
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Yi = g(Zi) + Wi, i = 1,..., n, where we wish to estimate the function g given the data under the assumption that the Wi are independent indentically distributed Gaussian error terms and g lies inside of some function space
A generalized Dantzig selector with shrinkage tuning
 Biometrika
, 2009
"... The Dantzig selector performs variable selection and model fitting in linear regression. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the Lasso. While both the Lasso and Dantzig selector potentially do a good job of selecting the correct variables ..."
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Cited by 19 (7 self)
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The Dantzig selector performs variable selection and model fitting in linear regression. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the Lasso. While both the Lasso and Dantzig selector potentially do a good job of selecting the correct
THE DANTZIG SELECTOR IN COX’S PROPORTIONAL HAZARDS MODEL
"... The Dantzig Selector is a recent approach to estimation in highdimensional linear regression models with a large number of explanatory variables and a relatively small number of observations. As in the least absolute shrinkage and selection operator (LASSO), this approach sets certain regression co ..."
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Cited by 7 (1 self)
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The Dantzig Selector is a recent approach to estimation in highdimensional linear regression models with a large number of explanatory variables and a relatively small number of observations. As in the least absolute shrinkage and selection operator (LASSO), this approach sets certain regression
Analysis of Supersaturated Designs via the Dantzig Selector
, 2008
"... Abstract: A supersaturated design is a design whose run size is not enough for estimating all the main effects. It is commonly used in screening experiments, where the goals are to identify sparse and dominant active factors with low cost. In this paper, we study a variable selection method via the ..."
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Cited by 10 (2 self)
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the Dantzig selector, proposed by Candes and Tao (2007), to screen important effects. A graphical procedure and an automated procedure are suggested to accompany with the method. Simulation shows that this method performs well compared to existing methods in the literature and is more efficient at estimating
Generalized Dantzig Selector: Application to the ksupport norm
"... We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is desi ..."
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Cited by 4 (4 self)
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We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework
Discussion: “The Dantzig selector: Statistical estimation when p is much larger than n,” by E. Candes and
 IEEE Trans. Signal Process
, 2007
"... Professors Candès and Tao are to be congratulated for their innovative and valuable contribution to highdimensional sparse recovery and model selection. The analysis of vast data sets now commonly arising in scientific investigations poses many statistical challenges not present in smaller scale st ..."
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Cited by 7 (5 self)
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Professors Candès and Tao are to be congratulated for their innovative and valuable contribution to highdimensional sparse recovery and model selection. The analysis of vast data sets now commonly arising in scientific investigations poses many statistical challenges not present in smaller scale
Optimal designs for lasso and dantzig selector using expander codes. Arxiv preprint arXiv:1010.2457v5
, 2013
"... ABSTRACT. We investigate the highdimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the `2prediction error and the `1risk of the lasso and the Dantzig selector are optimal up to an explicit multiplicative constant. Thus we can estim ..."
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Cited by 2 (1 self)
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ABSTRACT. We investigate the highdimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the `2prediction error and the `1risk of the lasso and the Dantzig selector are optimal up to an explicit multiplicative constant. Thus we can
Variable Selection with The Modified Buckley–James Method and The Dantzig Selector for High–dimensional Survival Data
"... We develop a group of algorithms for variable selection using the accelerated failure time (AFT) models that are based on the synthesis of the Buckley–James estimating method and the Dantzig selector. In particular, first two algorithms are based on two modified Buckley–James estimating methods that ..."
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We develop a group of algorithms for variable selection using the accelerated failure time (AFT) models that are based on the synthesis of the Buckley–James estimating method and the Dantzig selector. In particular, first two algorithms are based on two modified Buckley–James estimating methods
Printed in Great Britain A generalized Dantzig selector with shrinkage tuning
"... The Dantzig selector performs variable selection and model fitting in linear regression. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the lasso. While both the lasso and Dantzig selector potentially do a good job of selecting the correct variables ..."
Abstract
 Add to MetaCart
The Dantzig selector performs variable selection and model fitting in linear regression. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the lasso. While both the lasso and Dantzig selector potentially do a good job of selecting the correct
Results 11  20
of
113