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Continuous Generalized Gradient Descent

by Cun-hui Zhang
"... This article derives characterizations and computational algorithms for continuous general gradient descent trajectories in high-dimensional parameter spaces for statistical model selection, prediction, and classification. Examples include proportional gradient shrinkage as an extension of LASSO and ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
This article derives characterizations and computational algorithms for continuous general gradient descent trajectories in high-dimensional parameter spaces for statistical model selection, prediction, and classification. Examples include proportional gradient shrinkage as an extension of LASSO

cggd Fits Continuous Generalized Gradient Descent models

by Cun-hui Zhang, Ofer Melnik, Maintainer Cun-hui Zhang, Needscompilation No , 2015
"... Description Efficient procedures for fitting an entire regression ..."
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Description Efficient procedures for fitting an entire regression

Greedy Function Approximation: A Gradient Boosting Machine

by Jerome H. Friedman - Annals of Statistics , 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
Abstract - Cited by 1000 (13 self) - Add to MetaCart
Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed

Learning to rank using gradient descent

by Chris Burges, Tal Shaked, Erin Renshaw, Matt Deeds, Nicole Hamilton, Greg Hullender - In ICML , 2005
"... We investigate using gradient descent methods for learning ranking functions; we propose a simple probabilistic cost function, and we introduce RankNet, an implementation of these ideas using a neural network to model the underlying ranking function. We present test results on toy data and on data f ..."
Abstract - Cited by 534 (17 self) - Add to MetaCart
We investigate using gradient descent methods for learning ranking functions; we propose a simple probabilistic cost function, and we introduce RankNet, an implementation of these ideas using a neural network to model the underlying ranking function. We present test results on toy data and on data

Regularization paths for generalized linear models via coordinate descent

by Jerome Friedman, Trevor Hastie, Rob Tibshirani , 2009
"... We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, twoclass logistic regression, and multinomial regression problems while the penalties include ℓ1 (the lasso), ℓ2 (ridge regression) and mixtures of the two (the elastic ..."
Abstract - Cited by 724 (15 self) - Add to MetaCart
We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, twoclass logistic regression, and multinomial regression problems while the penalties include ℓ1 (the lasso), ℓ2 (ridge regression) and mixtures of the two (the

Pegasos: Primal Estimated sub-gradient solver for SVM

by Shai Shalev-Shwartz, Yoram Singer, Nathan Srebro, Andrew Cotter
"... We describe and analyze a simple and effective stochastic sub-gradient 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 ..."
Abstract - Cited by 542 (20 self) - Add to MetaCart
We describe and analyze a simple and effective stochastic sub-gradient 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

Learning Long-Term Dependencies with Gradient Descent is Difficult

by Yoshua Bengio, Patrice Simard, Paolo Frasconi - TO APPEAR IN THE SPECIAL ISSUE ON RECURRENT NETWORKS OF THE IEEE TRANSACTIONS ON NEURAL NETWORKS
"... Recurrent neural networks can be used to map input sequences to output sequences, such as for recognition, production or prediction problems. However, practical difficulties have been reported in training recurrent neural networks to perform tasks in which the temporal contingencies present in th ..."
Abstract - Cited by 389 (37 self) - Add to MetaCart
in the input/output sequences span long intervals. We showwhy gradient based learning algorithms face an increasingly difficult problem as the duration of the dependencies to be captured increases. These results expose a trade-off between efficient learning by gradient descent and latching on information

Multipoint quantitative-trait linkage analysis in general pedigrees

by Laura Almasy, John Blangero - Am. J. Hum. Genet , 1998
"... Multipoint linkage analysis of quantitative-trait loci (QTLs) has previously been restricted to sibships and small pedigrees. In this article, we show how variance-component linkage methods can be used in pedigrees of arbitrary size and complexity, and we develop a general framework for multipoint i ..."
Abstract - Cited by 567 (60 self) - Add to MetaCart
identity-by-descent (IBD) probability calculations. We extend the sib-pair multi-point mapping approach of Fulker et al. to general rel-ative pairs. This multipoint IBD method uses the pro-portion of alleles shared identical by descent at genotyped loci to estimate IBD sharing at arbitrary points along a

Algorithms for Non-negative Matrix Factorization

by Daniel D. Lee, H. Sebastian Seung - In NIPS , 2001
"... Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minim ..."
Abstract - Cited by 1246 (5 self) - Add to MetaCart
. The algorithms can also be interpreted as diagonally rescaled gradient descent, where the rescaling factor is optimally chosen to ensure convergence.

Coverage Control for Mobile Sensing Networks

by Jorge Cortes, Sonia Martínez, Timur Karatas, Francesco Bullo , 2002
"... This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functio ..."
Abstract - Cited by 582 (49 self) - Add to MetaCart
This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility
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