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83,671
The Mathematics of Statistical Machine Translation: Parameter Estimation
 COMPUTATIONAL LINGUISTICS
, 1993
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A gentle tutorial on the EM algorithm and its application to parameter estimation for gaussian mixture and hidden markov models
, 1997
"... We describe the maximumlikelihood parameter estimation problem and how the Expectationform of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2) fi ..."
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Cited by 693 (4 self)
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We describe the maximumlikelihood parameter estimation problem and how the Expectationform of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2
Pegasos: Primal Estimated subgradient solver for SVM
"... We describe and analyze a simple and effective stochastic subgradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy ɛ is Õ(1/ɛ), where each iteration operates on a singl ..."
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Cited by 542 (20 self)
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single training example. In contrast, previous analyses of stochastic gradient descent methods for SVMs require Ω(1/ɛ2) iterations. As in previously devised SVM solvers, the number of iterations also scales linearly with 1/λ, where λ is the regularization parameter of SVM. For a linear kernel, the total
A HeteroskedasticityConsistent Covariance Matrix Estimator And A Direct Test For Heteroskedasticity
, 1980
"... This paper presents a parameter covariance matrix estimator which is consistent even when the disturbances of a linear regression model are heteroskedastic. This estimator does not depend on a formal model of the structure of the heteroskedasticity. By comparing the elements of the new estimator ..."
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Cited by 3211 (5 self)
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This paper presents a parameter covariance matrix estimator which is consistent even when the disturbances of a linear regression model are heteroskedastic. This estimator does not depend on a formal model of the structure of the heteroskedasticity. By comparing the elements of the new estimator
The Dantzig selector: statistical estimation when p is much larger than n
, 2005
"... In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n ≪ ..."
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Cited by 879 (14 self)
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In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n
A Study of CrossValidation and Bootstrap for Accuracy Estimation and Model Selection
 INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1995
"... We review accuracy estimation methods and compare the two most common methods: crossvalidation and bootstrap. Recent experimental results on artificial data and theoretical results in restricted settings have shown that for selecting a good classifier from a set of classifiers (model selection), te ..."
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Cited by 1283 (11 self)
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), tenfold crossvalidation may be better than the more expensive leaveoneout crossvalidation. We report on a largescale experiment  over half a million runs of C4.5 and a NaiveBayes algorithm  to estimate the effects of different parameters on these algorithms on realworld datasets. For cross
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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of the proposed penalized likelihood estimators are established. Furthermore, with proper choice of regularization parameters, we show that the proposed estimators perform as well as the oracle procedure in variable selection; namely, they work as well as if the correct submodel were known. Our simulation shows
Choosing multiple parameters for support vector machines
 MACHINE LEARNING
, 2002
"... The problem of automatically tuning multiple parameters for pattern recognition Support Vector Machines (SVMs) is considered. This is done by minimizing some estimates of the generalization error of SVMs using a gradient descent algorithm over the set of parameters. Usual methods for choosing para ..."
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Cited by 470 (17 self)
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The problem of automatically tuning multiple parameters for pattern recognition Support Vector Machines (SVMs) is considered. This is done by minimizing some estimates of the generalization error of SVMs using a gradient descent algorithm over the set of parameters. Usual methods for choosing
Longitudinal data analysis using generalized linear models”.
 Biometrika,
, 1986
"... SUMMARY This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating ..."
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Cited by 1526 (8 self)
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SUMMARY This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence
Probabilistic Principal Component Analysis
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 1999
"... Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximumlikelihood estimation of paramet ..."
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Cited by 709 (5 self)
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of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss, with illustrative examples, the advantages conveyed by this probabilistic approach
Results 1  10
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83,671