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549
Largescale Matrix Factorization with Distributed Stochastic Gradient Descent
 In KDD
, 2011
"... We provide a novel algorithm to approximately factor large matrices with millions of rows, millions of columns, and billions of nonzero elements. Our approach rests on stochastic gradient descent (SGD), an iterative stochastic optimization algorithm. Based on a novel “stratified ” variant of SGD, we ..."
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Cited by 68 (7 self)
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We provide a novel algorithm to approximately factor large matrices with millions of rows, millions of columns, and billions of nonzero elements. Our approach rests on stochastic gradient descent (SGD), an iterative stochastic optimization algorithm. Based on a novel “stratified ” variant of SGD, we obtain a new matrixfactorization algorithm, called DSGD, that can be fully distributed and run on webscale datasets using, e.g., MapReduce. DSGD can handle a wide variety of matrix factorizations and has good scalability properties. 1
2004), Applying conditional random fields to Japanese morphological analysis
 in Proceedings of Conference on Empirical Methods on Natural Language Processing
, 2004
"... This paper presents Japanese morphological analysis based on conditional random fields (CRFs). Previous work in CRFs assumed that observation sequence (word) boundaries were fixed. However, word boundaries are not clear in Japanese, and hence a straightforward application of CRFs is not possible. ..."
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Cited by 63 (2 self)
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This paper presents Japanese morphological analysis based on conditional random fields (CRFs). Previous work in CRFs assumed that observation sequence (word) boundaries were fixed. However, word boundaries are not clear in Japanese, and hence a straightforward application of CRFs is not possible. We show how CRFs can be applied to situations where word boundary ambiguity exists. CRFs offer a solution to the longstanding problems in corpusbased or statistical Japanese morphological analysis. First, flexible feature designs for hierarchical tagsets become possible. Second, influences of label and length bias are minimized. We experiment CRFs on the standard testbed corpus used for Japanese morphological analysis, and evaluate our results using the same experimental dataset as the HMMs and MEMMs previously reported in this task. Our results confirm that CRFs not only solve the longstanding problems but also improve the performance over HMMs and MEMMs. 1
Calibrating Volatility Surfaces Via RelativeEntropy Minimization
 Applied Mathematical Finance
, 1997
"... We present a framework for calibrating a pricing model to a prescribed set of option prices quoted... ..."
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Cited by 62 (2 self)
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We present a framework for calibrating a pricing model to a prescribed set of option prices quoted...
LargeScale ActiveSet BoxConstrained Optimization Method with Spectral Projected Gradients
 Computational Optimization and Applications
, 2001
"... A new activeset method for smooth boxconstrained minimization is introduced. The algorithm combines an unconstrained method, including a new linesearch which aims to add many constraints to the working set at a single iteration, with a recently introduced technique (spectral projected gradien ..."
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Cited by 62 (11 self)
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A new activeset method for smooth boxconstrained minimization is introduced. The algorithm combines an unconstrained method, including a new linesearch which aims to add many constraints to the working set at a single iteration, with a recently introduced technique (spectral projected gradient) for dropping constraints from the working set. Global convergence is proved. A computer implementation is fully described and a numerical comparison assesses the reliability of the new algorithm. Keywords: Boxconstrained minimization, numerical methods, activeset strategies, Spectral Projected Gradient. 1
LBFGSB  Fortran Subroutines for LargeScale Bound Constrained Optimization
, 1994
"... LBFGSB is a limited memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. It is intended for problems in which information on the Hessian matrix is di cult to obtain, or for large dense problems. LBFGSB can also be used for unconstrained pr ..."
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Cited by 57 (3 self)
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LBFGSB is a limited memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. It is intended for problems in which information on the Hessian matrix is di cult to obtain, or for large dense problems. LBFGSB can also be used for unconstrained problems, and in this case performs similarly to its predecessor, algorithm LBFGS (Harwell routine VA15). The algorithm is implemented in Fortran 77.
Fast sweeping methods for static hamiltonjacobi equations
 Society for Industrial and Applied Mathematics
, 2005
"... Abstract. We propose a new sweeping algorithm which discretizes the Legendre transform of the numerical Hamiltonian using an explicit formula. This formula yields the numerical solution at a grid point using only its immediate neighboring grid values and is easy to implement numerically. The minimiz ..."
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Cited by 54 (5 self)
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Abstract. We propose a new sweeping algorithm which discretizes the Legendre transform of the numerical Hamiltonian using an explicit formula. This formula yields the numerical solution at a grid point using only its immediate neighboring grid values and is easy to implement numerically. The minimization that is related to the Legendre transform in our sweeping scheme can either be solved analytically or numerically. We illustrate the efficiency and accuracy approach with several numerical examples in two and three dimensions.
A comparison of optimization methods and software for largescale l1regularized linear classification
 The Journal of Machine Learning Research
"... Largescale linear classification is widely used in many areas. The L1regularized form can be applied for feature selection; however, its nondifferentiability causes more difficulties in training. Although various optimization methods have been proposed in recent years, these have not yet been com ..."
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Cited by 53 (7 self)
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Largescale linear classification is widely used in many areas. The L1regularized form can be applied for feature selection; however, its nondifferentiability causes more difficulties in training. Although various optimization methods have been proposed in recent years, these have not yet been compared suitably. In this paper, we first broadly review existing methods. Then, we discuss stateoftheart software packages in detail and propose two efficient implementations. Extensive comparisons indicate that carefully implemented coordinate descent methods are very suitable for training large document data.
Optimizing costly functions with simple constraints: A limitedmemory projected quasinewton algorithm
 Proc. of Conf. on Artificial Intelligence and Statistics
, 2009
"... An optimization algorithm for minimizing a smooth function over a convex set is described. Each iteration of the method computes a descent direction by minimizing, over the original constraints, a diagonal plus lowrank quadratic approximation to the function. The quadratic approximation is construct ..."
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Cited by 51 (9 self)
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An optimization algorithm for minimizing a smooth function over a convex set is described. Each iteration of the method computes a descent direction by minimizing, over the original constraints, a diagonal plus lowrank quadratic approximation to the function. The quadratic approximation is constructed using a limitedmemory quasiNewton update. The method is suitable for largescale problems where evaluation of the function is substantially more expensive than projection onto the constraint set. Numerical experiments on onenorm regularized test problems indicate that the proposed method is competitive with stateoftheart methods such as boundconstrained LBFGS and orthantwise descent. We further show that the method generalizes to a wide class of problems, and substantially improves on stateoftheart methods for problems such as learning the structure of Gaussian graphical models and Markov random fields. 1
Identifying functional modules in proteinprotein interaction networks: an integrated exact approach
 Bioinformatics
, 2008
"... Motivation: With the exponential growth of expression and proteinprotein interaction (PPI) data, the frontier of research in system biology shifts more and more to the integrated analysis of these large datasets. Of particular interest is the identification of functional modules in PPI networks, sha ..."
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Cited by 47 (4 self)
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Motivation: With the exponential growth of expression and proteinprotein interaction (PPI) data, the frontier of research in system biology shifts more and more to the integrated analysis of these large datasets. Of particular interest is the identification of functional modules in PPI networks, sharing common cellular function beyond the scope of classical pathways, by means of detecting differentially expressed regions in PPI networks. This requires on the one hand an adequate scoring of the nodes in the network to be identified and on the other hand the availability of an effective algorithm to find the maximally scoring network regions. Various heuristic approaches have been proposed in the literature. Results: Here we present the first exact solution for this problem, which is based on integer linear programming and its connection to the wellknown prizecollecting Steiner tree problem from Operations