Results 1  10
of
399,578
A note on elementwise matrix sparsification via a matrixvalued Bernstein inequality
 Inform. Process. Lett
"... ar ..."
Low Rank Matrixvalued Chernoff Bounds and Approximate Matrix Multiplication
"... In this paper we develop algorithms for approximating matrix multiplication with respect to the spectral norm. Let A ∈ R n×m and B ∈ R n×p be two matrices and ε>0. We approximate the product A ⊤ B using two sketches e A ∈ R t×m and e B ∈ R t×p,wheret≪n, such that ‚ eA ⊤ eB − A ⊤ B ‚ ≤ ε ‖A‖2 ‖B‖ ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
that depend on the smaller parameter of stable rank this technology itself seems weak. However, we show that in combination with a simple truncation argument it is amenable to provide such bounds. To handle similar bounds for row sampling, we develop a novel matrixvalued Chernoff bound inequality which we
Spectral counting of triangles in powerlaw networks via elementwise sparsification
 In SODA ’02: Proceedings of the thirteenth annual ACMSIAM symposium on Discrete algorithms
, 2009
"... Triangle counting is an important problem in graph mining. The clustering coefficient and the transitivity ratio, two commonly used measures effectively quantify the triangle density in order to quantify the fact that friends of friends tend to be friends themselves. Furthermore, several successful ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
graph mining applications rely on the number of triangles. In this paper, we study the problem of counting triangles in large, powerlaw networks. Our algorithm, SPARSIFYINGEIGENTRIANGLE, relies on the spectral properties of powerlaw networks and the AchlioptasMcSherry sparsification process
A Limited Memory Algorithm for Bound Constrained Optimization
 SIAM Journal on Scientific Computing
, 1994
"... An algorithm for solving large nonlinear optimization problems with simple bounds is described. ..."
Abstract

Cited by 557 (9 self)
 Add to MetaCart
An algorithm for solving large nonlinear optimization problems with simple bounds is described.
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
Abstract

Cited by 780 (22 self)
 Add to MetaCart
is contained in the socalled kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input spaceclassical model selection
Symmetry and Related Properties via the Maximum Principle
, 1979
"... We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plan ..."
Abstract

Cited by 539 (4 self)
 Add to MetaCart
We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting
Regression Shrinkage and Selection Via the Lasso
 Journal of the Royal Statistical Society, Series B
, 1994
"... We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactl ..."
Abstract

Cited by 4055 (51 self)
 Add to MetaCart
We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients
Parametric Shape Analysis via 3Valued Logic
, 2001
"... Shape Analysis concerns the problem of determining "shape invariants"... ..."
Abstract

Cited by 660 (79 self)
 Add to MetaCart
Shape Analysis concerns the problem of determining "shape invariants"...
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
Abstract

Cited by 886 (35 self)
 Add to MetaCart
the variation in the perturbed quantity. Up to the higherorder terms that are ignored in the expansion, these statistics tend to be more realistic than perturbation bounds obtained in terms of norms. The technique is applied to a number of problems in matrix perturbation theory, including least squares
Results 1  10
of
399,578