Results 1  10
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3,184
Efficient sparse coding algorithms
 In NIPS
, 2007
"... Sparse coding provides a class of algorithms for finding succinct representations of stimuli; given only unlabeled input data, it discovers basis functions that capture higherlevel features in the data. However, finding sparse codes remains a very difficult computational problem. In this paper, we ..."
Abstract

Cited by 445 (14 self)
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significant speedup for sparse coding, allowing us to learn larger sparse codes than possible with previously described algorithms. We apply these algorithms to natural images and demonstrate that the inferred sparse codes exhibit endstopping and nonclassical receptive field surround suppression and
A General Theory of Equilibrium Selection in Games.
, 1988
"... Abstract This paper presents a Downsian model of political competition in which parties have incomplete but richer information than voters on policy effects. Each party can observe a private signal of the policy effects, while voters cannot. In this setting, voters infer the policy effects from the ..."
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Cited by 734 (4 self)
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of the Median Voter Theorem in the classical Downsian model. Our equilibrium analysis suggests similarity between the set of WPBEs in this model and the set of uniformly perfect equilibria of Harsanyi and Selten (1988) in the model with completely informed parties which we studied in a previous paper
Distortion invariant object recognition in the dynamic link architecture
 IEEE TRANSACTIONS ON COMPUTERS
, 1993
"... We present an object recognition system based on the Dynamic Link Architecture, which is an extension to classical Artificial Neural Networks. The Dynamic Link Architecture exploits correlations in the finescale temporal structure of cellular signals in order to group neurons dynamically into hig ..."
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Cited by 637 (80 self)
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We present an object recognition system based on the Dynamic Link Architecture, which is an extension to classical Artificial Neural Networks. The Dynamic Link Architecture exploits correlations in the finescale temporal structure of cellular signals in order to group neurons dynamically
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 547 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
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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, where r is the residual vector y − A˜x and t is a positive scalar. We show that if A obeys a uniform uncertainty principle (with unitnormed columns) and if the true parameter vector x is sufficiently sparse (which here roughly guarantees that the model is identifiable), then with very large probability
Decoding by Linear Programming
, 2004
"... This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to rec ..."
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Cited by 1399 (16 self)
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This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible
New tight frames of curvelets and optimal representations of objects with piecewise C² singularities
 COMM. ON PURE AND APPL. MATH
, 2002
"... This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges. Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needleshap ..."
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Cited by 428 (21 self)
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This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges. Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needle
Sparse signal reconstruction from limited data using FOCUSS: A reweighted minimum norm algorithm
 IEEE TRANS. SIGNAL PROCESSING
, 1997
"... We present a nonparametric algorithm for finding localized energy solutions from limited data. The problem we address is underdetermined, and no prior knowledge of the shape of the region on which the solution is nonzero is assumed. Termed the FOcal Underdetermined System Solver (FOCUSS), the algor ..."
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Cited by 368 (22 self)
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view of the algorithm as a novel optimization method which combines desirable characteristics of both classical optimization and learningbased algorithms is provided. Mathematical results on conditions for uniqueness of sparse solutions are also given. Applications of the algorithm are illustrated
A New Efficient Algorithm for Computing Gröbner Bases (F4)
 IN: ISSAC ’02: PROCEEDINGS OF THE 2002 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION
, 2002
"... This paper introduces a new efficient algorithm for computing Gröbner bases. To avoid as much as possible intermediate computation, the algorithm computes successive truncated Gröbner bases and it replaces the classical polynomial reduction found in the Buchberger algorithm by the simultaneous reduc ..."
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Cited by 365 (57 self)
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This paper introduces a new efficient algorithm for computing Gröbner bases. To avoid as much as possible intermediate computation, the algorithm computes successive truncated Gröbner bases and it replaces the classical polynomial reduction found in the Buchberger algorithm by the simultaneous
A review of algebraic multigrid
, 2001
"... Since the early 1990s, there has been a strongly increasing demand for more efficient methods to solve large sparse, unstructured linear systems of equations. For practically relevant problem sizes, classical onelevel methods had already reached their limits and new hierarchical algorithms had to b ..."
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Cited by 347 (11 self)
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Since the early 1990s, there has been a strongly increasing demand for more efficient methods to solve large sparse, unstructured linear systems of equations. For practically relevant problem sizes, classical onelevel methods had already reached their limits and new hierarchical algorithms had
Results 1  10
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