Results 11  20
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5,093
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
, 2001
"... Variable selection is fundamental to highdimensional 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 ..."
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Cited by 948 (62 self)
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Variable selection is fundamental to highdimensional 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
Training Linear SVMs in Linear Time
, 2006
"... Linear Support Vector Machines (SVMs) have become one of the most prominent machine learning techniques for highdimensional sparse data commonly encountered in applications like text classification, wordsense disambiguation, and drug design. These applications involve a large number of examples n ..."
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Cited by 549 (6 self)
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Linear Support Vector Machines (SVMs) have become one of the most prominent machine learning techniques for highdimensional sparse data commonly encountered in applications like text classification, wordsense disambiguation, and drug design. These applications involve a large number of examples n
Mean shift: A robust approach toward feature space analysis
 In PAMI
, 2002
"... A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data the convergence ..."
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Cited by 2395 (37 self)
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A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data
SIMULTANEOUS ANALYSIS OF LASSO AND DANTZIG SELECTOR
 SUBMITTED TO THE ANNALS OF STATISTICS
, 2007
"... We exhibit an approximate equivalence between the Lasso estimator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the ℓp estimation loss for 1 ≤ p ≤ 2 in the linear model when th ..."
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Cited by 472 (11 self)
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We exhibit an approximate equivalence between the Lasso estimator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the ℓp estimation loss for 1 ≤ p ≤ 2 in the linear model when
Highdimensional regression with unknown variance
 SUBMITTED TO THE STATISTICAL SCIENCE
, 2012
"... We review recent results for highdimensional sparse linear regression in the practical case of unknown variance. Different sparsity settings are covered, including coordinatesparsity, groupsparsity and variationsparsity. The emphasis is put on nonasymptotic analyses and feasible procedures. In ..."
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Cited by 10 (1 self)
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We review recent results for highdimensional sparse linear regression in the practical case of unknown variance. Different sparsity settings are covered, including coordinatesparsity, groupsparsity and variationsparsity. The emphasis is put on nonasymptotic analyses and feasible procedures
Bayesian Backfitting for HighDimensional Regression
"... We present an algorithm aimed at addressing both computational and analytical intractability of Bayesian regression models which operate in very highdimensional, usually underconstrained spaces. Several domains of research frequently provide such datasets, including chemometrics [2], and human move ..."
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We present an algorithm aimed at addressing both computational and analytical intractability of Bayesian regression models which operate in very highdimensional, usually underconstrained spaces. Several domains of research frequently provide such datasets, including chemometrics [2], and human
Support Vector Machines for Classification and Regression
 UNIVERSITY OF SOUTHAMPTON, TECHNICAL REPORT
, 1998
"... The problem of empirical data modelling is germane to many engineering applications.
In empirical data modelling a process of induction is used to build up a model of the
system, from which it is hoped to deduce responses of the system that have yet to be observed.
Ultimately the quantity and qualit ..."
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Cited by 357 (5 self)
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and quality of the observations govern the performance
of this empirical model. By its observational nature data obtained is finite and sampled;
typically this sampling is nonuniform and due to the high dimensional nature of the
problem the data will form only a sparse distribution in the input space
Flexible smoothing with Bsplines and penalties
 STATISTICAL SCIENCE
, 1996
"... Bsplines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots ..."
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Cited by 405 (7 self)
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splines and propose various criteria for the choice of an optimal penalty parameter. Nonparametric logistic regression, density estimation and scatterplot smoothing are used as examples. Some details of the computations are presented.
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
Results 11  20
of
5,093