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10,625
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 568 (10 self)
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that for large n, and for all Φ’s except a negligible fraction, the following property holds: For every y having a representation y = Φα0 by a coefficient vector α0 ∈ R m with fewer than ρ · n nonzeros, the solution α1 of the ℓ 1 minimization problem min �x�1 subject to Φα = y is unique and equal to α0
ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
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Cited by 2728 (61 self)
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The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods
Least angle regression
, 2004
"... The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to s ..."
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Cited by 1326 (37 self)
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The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope
Estimation of probabilities from sparse data for the language model component of a speech recognizer
 IEEE Transactions on Acoustics, Speech and Signal Processing
, 1987
"... AbstractThe description of a novel type of rngram language model is given. The model offers, via a nonlinear recursive procedure, a computation and space efficient solution to the problem of estimating probabilities from sparse data. This solution compares favorably to other proposed methods. Wh ..."
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Cited by 799 (2 self)
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, and it is a problem that one always encounters while collecting frequency statistics on words and word sequences (mgrams) from a text of finite size. This means that even for a very large data collection, the maximum likelihood estimation method does not allow Turing’s estimate PT for a probability of a
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 483 (2 self)
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This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination
MINIMAL VANISHING SUMS OF ROOTS OF UNITY WITH LARGE COEFFICIENTS
"... A vanishing sum a0 + a1ζn +... + an−1ζ n−1 n = 0 where ζn is a primitive nth root of unity and the ai’s are nonnegative integers is called minimal if the coefficient vector (a0,..., an−1) does not properly dominate the coefficient vector of any other such nonzero sum. We show that for every c ∈ N t ..."
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Cited by 14 (7 self)
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A vanishing sum a0 + a1ζn +... + an−1ζ n−1 n = 0 where ζn is a primitive nth root of unity and the ai’s are nonnegative integers is called minimal if the coefficient vector (a0,..., an−1) does not properly dominate the coefficient vector of any other such nonzero sum. We show that for every c ∈ N
Multiple kernel learning, conic duality, and the SMO algorithm
 In Proceedings of the 21st International Conference on Machine Learning (ICML
, 2004
"... While classical kernelbased classifiers are based on a single kernel, in practice it is often desirable to base classifiers on combinations of multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for the support vector machine (SVM), and showed that the optimiz ..."
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Cited by 445 (31 self)
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that the optimization of the coefficients of such a combination reduces to a convex optimization problem known as a quadraticallyconstrained quadratic program (QCQP). Unfortunately, current convex optimization toolboxes can solve this problem only for a small number of kernels and a small number of data points
Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure
, 2004
"... This paper presents a new approach to estimation and inference in panel data models with a multifactor error structure where the unobserved common factors are (possibly) correlated with exogenously given individualspecific regressors, and the factor loadings differ over the cross section units. The ..."
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Cited by 383 (44 self)
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that concerns the coefficients of the individualspecific regressors, and the other that focusses on the mean of the individual coefficients assumed random. In both cases appropriate estimators, referred to as common correlated effects (CCE) estimators, are proposed and their asymptotic distribution as N
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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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
Results 1  10
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10,625