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199
Regression Shrinkage and Selection Via the Lasso
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 1994
"... We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactl ..."
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Cited by 4212 (49 self)
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an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and treebased models are briefly described.
The group Lasso for logistic regression
 Journal of the Royal Statistical Society, Series B
, 2008
"... Summary. The group lasso is an extension of the lasso to do variable selection on (predefined) groups of variables in linear regression models. The estimates have the attractive property of being invariant under groupwise orthogonal reparameterizations. We extend the group lasso to logistic regressi ..."
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Cited by 276 (11 self)
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regression models and present an efficient algorithm, that is especially suitable for high dimensional problems, which can also be applied to generalized linear models to solve the corresponding convex optimization problem. The group lasso estimator for logistic regression is shown to be statistically
SPIKE DETECTION FROM INACCURATE SAMPLINGS
"... Abstract. This article investigates the superresolution phenomenon using the celebrated statistical estimator LASSO in the complex valued measure framework. More precisely, we study the recovery of a discrete measure (spike train) from few noisy observations (Fourier samples, moments, Stieltjes tra ..."
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Cited by 5 (0 self)
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Abstract. This article investigates the superresolution phenomenon using the celebrated statistical estimator LASSO in the complex valued measure framework. More precisely, we study the recovery of a discrete measure (spike train) from few noisy observations (Fourier samples, moments, Stieltjes
The Constrained Lasso
"... Motivated by applications in areas as diverse as finance, image reconstruction, and curve estimation, we introduce the constrained lasso problem, where the underlying parameters satisfy a collection of linear constraints. We show that many statistical methods, such as the fused lasso, monotone curve ..."
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Cited by 1 (0 self)
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Motivated by applications in areas as diverse as finance, image reconstruction, and curve estimation, we introduce the constrained lasso problem, where the underlying parameters satisfy a collection of linear constraints. We show that many statistical methods, such as the fused lasso, monotone
Largescale bayesian logistic regression for text categorization
 Technometrics
"... Logistic regression analysis of highdimensional data, such as natural language text, poses computational and statistical challenges. Maximum likelihood estimation often fails in these applications. We present a simple Bayesian logistic regression approach that uses a Laplace prior to avoid overfitt ..."
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Cited by 191 (13 self)
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Logistic regression analysis of highdimensional data, such as natural language text, poses computational and statistical challenges. Maximum likelihood estimation often fails in these applications. We present a simple Bayesian logistic regression approach that uses a Laplace prior to avoid
On the Distribution of the Adaptive LASSO
, 2007
"... We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the largesample limit. The largesample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where ..."
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the estimator is tuned to perform consistent model selection. In particular, these results question the statistical relevance of the ‘oracle ’ property of the adaptive LASSO estimator established in Zou (2006). Moreover, we also provide an impossibility result regarding the estimation of the distribution
Sparse estimation of large covariance matrices via a nested Lasso penalty. Annals of Applied Statistics
, 2007
"... The paper proposes a new covariance estimator for large covariance matrices when the variables have a natural ordering. Using the Cholesky decomposition of the inverse, we impose a banded structure on the Cholesky factor, and select the bandwidth adaptively for each row of the Cholesky factor, using ..."
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Cited by 57 (8 self)
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, using a novel penalty we call nested Lasso. This structure has more flexibility than regular banding, but, unlike regular Lasso applied to the entries of the Cholesky factor, results in a sparse estimator for the inverse of the covariance matrix. An iterative algorithm for solving the optimization
The Deterministic Bayesian Lasso
, 2014
"... The application of the lasso is espoused in highdimensional settings where only a small number of the regression coefficients are believed to be nonzero (i.e., the solution is sparse). Moreover, statistical properties of highdimensional lasso estimators are often proved under the assumption that ..."
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The application of the lasso is espoused in highdimensional settings where only a small number of the regression coefficients are believed to be nonzero (i.e., the solution is sparse). Moreover, statistical properties of highdimensional lasso estimators are often proved under the assumption
Highdimensional data and the Lasso
, 2013
"... How would you try to solve a linear system of equations with more unknowns than equations? Of course, there are infinitely many solutions, and yet this is the sort of the problem statisticians face with many modern datasets, arising in genetics, imaging, finance and many other fields. What’s worse, ..."
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, our equations are often corrupted by noisy measurements! In this article we will introduce a statistical method that has been at the centre of the huge amount of research that has gone into solving these problems. We’ll begin by reviewing the classical version of the problems, before moving
Submitted to the Annals of Statistics ADAPTIVE TESTING FOR THE GRAPHICAL LASSO
"... We consider tests of significance in the setting of the graphical lasso for inverse covariance matrix estimation. We propose a simple test statistic based on a subsequence of the knots in the graphical lasso path. We show that this statistic has an exponential asymptotic null distribution, under the ..."
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We consider tests of significance in the setting of the graphical lasso for inverse covariance matrix estimation. We propose a simple test statistic based on a subsequence of the knots in the graphical lasso path. We show that this statistic has an exponential asymptotic null distribution, under
Results 1  10
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199