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78,339
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 4055 (51 self)
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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
Ideal spatial adaptation by wavelet shrinkage
 Biometrika
, 1994
"... With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline, or variable bandwidth kernel, to the unknown function. Estimation with the aid of an oracle o ers dramatic ad ..."
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Cited by 1251 (5 self)
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spline ts and piecewisepolynomial ts, when equipped with an oracle to select the knots, are not dramatically more powerful than selective wavelet reconstruction with an oracle. We develop a practical spatially adaptive method, RiskShrink, which works by shrinkage of empirical wavelet coe cients. Risk
On the Relation Between the Shrinkage Effect and a Shrinkage Method
"... this paper to explain the source of this shrinkage effect, to investigate its behaviour and to show that the shrinkage method proposed by van Houwelingen and le Cessie (1990) is just tailored to remove this shrinkage effect. We further point out the existence of alternative methods serving the same ..."
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Cited by 1 (1 self)
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this paper to explain the source of this shrinkage effect, to investigate its behaviour and to show that the shrinkage method proposed by van Houwelingen and le Cessie (1990) is just tailored to remove this shrinkage effect. We further point out the existence of alternative methods serving
A fast iterative shrinkagethresholding algorithm with application to . . .
, 2009
"... We consider the class of Iterative ShrinkageThresholding Algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods is attractive due to its simplicity, however, they are also known to converge quite slowly. In this paper we present a Fast Iterat ..."
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Cited by 1055 (8 self)
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We consider the class of Iterative ShrinkageThresholding Algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods is attractive due to its simplicity, however, they are also known to converge quite slowly. In this paper we present a Fast
Adapting to unknown smoothness via wavelet shrinkage
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1995
"... We attempt to recover a function of unknown smoothness from noisy, sampled data. We introduce a procedure, SureShrink, which suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: a threshold level is assigned to each dyadic resolution level by the princip ..."
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Cited by 990 (20 self)
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on the choice of mother wavelet. We know from a previous paper by the authors that traditional smoothing methods  kernels, splines, and orthogonal series estimates  even with optimal choices of the smoothing parameter, would be unable to perform
Shrinkage methods: Least angles regression and LassoOutline Least Angle regression
, 2009
"... Conclusion The problem and the notation Nagarajan Natarajan, vishvAs vAsuki Shrinkage methods: Least angles regression and LassoOutline ..."
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Conclusion The problem and the notation Nagarajan Natarajan, vishvAs vAsuki Shrinkage methods: Least angles regression and LassoOutline
AUTOMATIC PARAMETER SETTING FOR ITERATIVE SHRINKAGE METHODS
"... Linear inverse problems are very common in signal and image processing. Algorithms that solve such problems typically involve several unknown parameters that need to be tuned. Here we consider an iterated shrinkage method that is based on the separable surrogate functions (SSF) idea, which exploits ..."
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Cited by 8 (0 self)
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Linear inverse problems are very common in signal and image processing. Algorithms that solve such problems typically involve several unknown parameters that need to be tuned. Here we consider an iterated shrinkage method that is based on the separable surrogate functions (SSF) idea, which exploits
Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
 IEEE Journal of Selected Topics in Signal Processing
, 2007
"... Abstract—Many problems in signal processing and statistical inference involve finding sparse solutions to underdetermined, or illconditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ℓ2) error term combined wi ..."
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Cited by 524 (15 self)
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with a sparsenessinducing (ℓ1) regularization term.Basis pursuit, the least absolute shrinkage and selection operator (LASSO), waveletbased deconvolution, and compressed sensing are a few wellknown examples of this approach. This paper proposes gradient projection (GP) algorithms for the bound
Minimax Estimation via Wavelet Shrinkage
, 1992
"... We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coe cients. The shrinkage can be tuned to be nearly minim ..."
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Cited by 322 (32 self)
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We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coe cients. The shrinkage can be tuned to be nearly
Survey on Independent Component Analysis
 NEURAL COMPUTING SURVEYS
, 1999
"... A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the ..."
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Cited by 2241 (104 self)
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of the original data. Wellknown linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes
Results 1  10
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