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Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
, 2010
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Sparse matrix solvers on the GPU: conjugate gradients and multigrid
 ACM Trans. Graph
, 2003
"... Permission to make digital/hard copy of part of all of this work for personal or classroom use is granted without fee provided that the copies are not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication, and its date appear, and notice is given ..."
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Cited by 275 (3 self)
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Permission to make digital/hard copy of part of all of this work for personal or classroom use is granted without fee provided that the copies are not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication, and its date appear, and notice is given that copying is by permission
An interiorpoint method for largescale l1regularized logistic regression
 Journal of Machine Learning Research
, 2007
"... Logistic regression with ℓ1 regularization has been proposed as a promising method for feature selection in classification problems. In this paper we describe an efficient interiorpoint method for solving largescale ℓ1regularized logistic regression problems. Small problems with up to a thousand ..."
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Cited by 233 (8 self)
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Logistic regression with ℓ1 regularization has been proposed as a promising method for feature selection in classification problems. In this paper we describe an efficient interiorpoint method for solving largescale ℓ1regularized logistic regression problems. Small problems with up to a thousand or so features and examples can be solved in seconds on a PC; medium sized problems, with tens of thousands of features and examples, can be solved in tens of seconds (assuming some sparsity in the data). A variation on the basic method, that uses a preconditioned conjugate gradient method to compute the search step, can solve very large problems, with a million features and examples (e.g., the 20 Newsgroups data set), in a few minutes, on a PC. Using warmstart techniques, a good approximation of the entire regularization path can be computed much more efficiently than by solving a family of problems independently.
Proximal support vector machine classifiers
 Proceedings KDD2001: Knowledge Discovery and Data Mining
, 2001
"... Abstract—A new approach to support vector machine (SVM) classification is proposed wherein each of two data sets are proximal to one of two distinct planes that are not parallel to each other. Each plane is generated such that it is closest to one of the two data sets and as far as possible from the ..."
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Cited by 140 (16 self)
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Abstract—A new approach to support vector machine (SVM) classification is proposed wherein each of two data sets are proximal to one of two distinct planes that are not parallel to each other. Each plane is generated such that it is closest to one of the two data sets and as far as possible from the other data set. Each of the two nonparallel proximal planes is obtained by a single MATLAB command as the eigenvector corresponding to a smallest eigenvalue of a generalized eigenvalue problem. Classification by proximity to two distinct nonlinear surfaces generated by a nonlinear kernel also leads to two simple generalized eigenvalue problems. The effectiveness of the proposed method is demonstrated by tests on simple examples as well as on a number of public data sets. These examples show the advantages of the proposed approach in both computation time and test set correctness. Index Terms—Support vector machines, proximal classification, generalized eigenvalues. 1
SuperLU DIST: A scalable distributedmemory sparse direct solver for unsymmetric linear systems
 ACM Trans. Mathematical Software
, 2003
"... We present the main algorithmic features in the software package SuperLU DIST, a distributedmemory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with a focus on scalability issues, and demonstrate the software’s parallel performance and sc ..."
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Cited by 131 (19 self)
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We present the main algorithmic features in the software package SuperLU DIST, a distributedmemory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with a focus on scalability issues, and demonstrate the software’s parallel performance and scalability on current machines. The solver is based on sparse Gaussian elimination, with an innovative static pivoting strategy proposed earlier by the authors. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication patterns, which lets us exploit techniques used in parallel sparse Cholesky algorithms to better parallelize both LU decomposition and triangular solution on largescale distributed machines.
An Updated Set of Basic Linear Algebra Subprograms (BLAS)
 ACM Transactions on Mathematical Software
, 2001
"... This paper summarizes the BLAS Technical Forum Standard, a speci #cation of a set of kernel routines for linear algebra, historically called the Basic Linear Algebra Subprograms and commonly known as the BLAS. The complete standard can be found in #1#, and on the BLAS Technical Forum webpage #http: ..."
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Cited by 108 (7 self)
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This paper summarizes the BLAS Technical Forum Standard, a speci #cation of a set of kernel routines for linear algebra, historically called the Basic Linear Algebra Subprograms and commonly known as the BLAS. The complete standard can be found in #1#, and on the BLAS Technical Forum webpage #http:##www.netlib.org#blas#blastforum##
Texture mapping using surface flattening via multidimensional scaling
 IEEE Transactions on Visualization and Computer Graphics
, 2002
"... AbstractÐWe present a novel technique for texture mapping on arbitrary surfaces with minimal distortions by preserving the local and global structure of the texture. The recent introduction of the fast marching method on triangulated surfaces made it possible to compute a geodesic distance map from ..."
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Cited by 102 (23 self)
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AbstractÐWe present a novel technique for texture mapping on arbitrary surfaces with minimal distortions by preserving the local and global structure of the texture. The recent introduction of the fast marching method on triangulated surfaces made it possible to compute a geodesic distance map from a given surface point in O…n lg n † operations, where n is the number of triangles that represent the surface. We use this method to design a surface flattening approach based on multidimensional scaling �MDS). MDS is a family of methods that map a set of points into a finite dimensional flat �Euclidean) domain, where the only given data is the corresponding distances between every pair of points. The MDS mapping yields minimal changes of the distances between the corresponding points. We then solve an ªinverseº problem and map a flat texture patch onto the curved surface while preserving the structure of the texture. Index TermsÐTexture mapping, multidimensional scaling, fast marching method, Geodesic distance, Euclidean distance. æ 1
Random Cascades on Wavelet Trees and Their Use in Analyzing and Modeling Natural Images
 Applied and Computational Harmonic Analysis
, 2001
"... in signal and image processing, including image denoising, coding, and superresolution. # 2001 Academic Press 1. INTRODUCTION Stochastic models of natural images underlie a variety of applications in image processing and lowlevel computer vision, including image coding, denoising and 1 MW supp ..."
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Cited by 98 (16 self)
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in signal and image processing, including image denoising, coding, and superresolution. # 2001 Academic Press 1. INTRODUCTION Stochastic models of natural images underlie a variety of applications in image processing and lowlevel computer vision, including image coding, denoising and 1 MW supported by NSERC 1967 fellowship; AW and MW by AFOSR Grant F496209810349 and ONR Grant N0001491J1004. Address correspondence to MW. 2 ES supported by NSF Career Grant MIP9796040 and an Alfred P. Sloan fellowship. 89 10635203/01 $35.00 Copyright # 2001 by Academic Press All rights of reproduction in any form reserved. 90 WAINWRIGHT, SIMONCELLI, AND WILLSKY restoration, interpolation and synthesis. Accordingly, the past decade has witnessed an increasing amount of research devoted to developing stochastic models of images (e.g., [19, 38, 45, 48, 55]). Simultaneously, wavel
An Algebraic Approach to Practical and Scalable Overlay Network Monitoring
 IN ACM SIGCOMM
, 2004
"... Overlay network monitoring enables distributed Internet applications to detect and recover from path outages and periods of degraded performance within seconds. For an overlay network with n end hosts, existing systems either require O(n²) measurements, and thus lack scalability, or can only estima ..."
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Cited by 98 (9 self)
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Overlay network monitoring enables distributed Internet applications to detect and recover from path outages and periods of degraded performance within seconds. For an overlay network with n end hosts, existing systems either require O(n²) measurements, and thus lack scalability, or can only estimate the latency but not congestion or failures. Our earlier extended abstract [1] briefly proposes an algebraic approach that selectively monitors k linearly independent paths that can fully describe all the O(n²) paths. The loss rates and latency of these k paths can be used to estimate the loss rates and latency of all other paths. Our scheme only assumes knowledge of the underlying IP topology, with links dynamically varying between lossy and normal. In this
Robust minimum variance beamforming
 IEEE Transactions on Signal Processing
, 2005
"... Abstract—This paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response. Sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold. In our method, uncerta ..."
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Cited by 88 (10 self)
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Abstract—This paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response. Sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold. In our method, uncertainty in the array manifold is explicitly modeled via an ellipsoid that gives the possible values of the array for a particular look direction. We choose weights that minimize the total weighted power output of the array, subject to the constraint that the gain should exceed unity for all array responses in this ellipsoid. The robust weight selection process can be cast as a secondorder cone program that can be solved efficiently using Lagrange multiplier techniques. If the ellipsoid reduces to a single point, the method coincides with Capon’s method. We describe in detail several methods that can be used to derive an appropriate uncertainty ellipsoid for the array response. We form separate uncertainty ellipsoids for each component in the signal path (e.g., antenna, electronics) and then determine an aggregate uncertainty ellipsoid from these. We give new results for modeling the elementwise products of ellipsoids. We demonstrate the robust beamforming and the ellipsoidal modeling methods with several numerical examples. Index Terms—Ellipsoidal calculus, Hadamard product, robust beamforming, secondorder cone programming.