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6,438
An Algorithm for Approximating the Satisfiability Problem of Highlevel Conditions (Long Version)
, 2007
"... The satisfiability problem is the fundamental problem in proving the conflictfreeness of specifications, or in finding a counterexample for an invalid statement. In this paper, we present a nondeterministic, monotone algorithm for this undecidable problem on graphical conditions that is both corre ..."
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Cited by 1 (1 self)
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correct and complete, but in general not guaranteed to terminate. For a fragment of highlevel conditions, the algorithm terminates, hence it is able to decide. Instead of enumerating all possible objects of a category to approach the problem, the algorithm uses the input condition in a constructive way
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1211 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 585 (13 self)
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the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a “valid ” or “maxentnormal ” approximation. We describe the relationship between four different methods that can be used
Greed is Good: Algorithmic Results for Sparse Approximation
, 2004
"... This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal representa ..."
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Cited by 916 (9 self)
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This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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. Introduction The task of calculating posterior marginals on nodes in an arbitrary Bayesian network is known to be NP hard In this paper we investigate the approximation performance of "loopy belief propagation". This refers to using the wellknown Pearl polytree algorithm [12] on a Bayesian network
Localitysensitive hashing scheme based on pstable distributions
 In SCG ’04: Proceedings of the twentieth annual symposium on Computational geometry
, 2004
"... inÇÐÓ�Ò We present a novel LocalitySensitive Hashing scheme for the Approximate Nearest Neighbor Problem underÐÔnorm, based onÔstable distributions. Our scheme improves the running time of the earlier algorithm for the case of theÐnorm. It also yields the first known provably efficient approximate ..."
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Cited by 521 (8 self)
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inÇÐÓ�Ò We present a novel LocalitySensitive Hashing scheme for the Approximate Nearest Neighbor Problem underÐÔnorm, based onÔstable distributions. Our scheme improves the running time of the earlier algorithm for the case of theÐnorm. It also yields the first known provably efficient approximate
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
, 2001
"... Variable selection is fundamental to highdimensional statistical modeling, including nonparametric regression. Many approaches in use are stepwise selection procedures, which can be computationally expensive and ignore stochastic errors in the variable selection process. In this article, penalized ..."
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Cited by 948 (62 self)
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functions are symmetric, nonconcave on (0, ∞), and have singularities at the origin to produce sparse solutions. Furthermore, the penalty functions should be bounded by a constant to reduce bias and satisfy certain conditions to yield continuous solutions. A new algorithm is proposed for optimizing
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 414 (21 self)
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We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 483 (2 self)
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that has been contaminated with additive noise, the goal is to identify which elementary signals participated and to approximate their coefficients. Although many algorithms have been proposed, there is little theory which guarantees that these algorithms can accurately and efficiently solve the problem
Clustering Gene Expression Patterns
, 1999
"... Recent advances in biotechnology allow researchers to measure expression levels for thousands of genes simultaneously, across different conditions and over time. Analysis of data produced by such experiments offers potential insight into gene function and regulatory mechanisms. A key step in the ana ..."
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Cited by 451 (11 self)
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in the analysis of gene expression data is the detection of groups of genes that manifest similar expression patterns. The corresponding algorithmic problem is to cluster multicondition gene expression patterns. In this paper we describe a novel clustering algorithm that was developed for analysis of gene
Results 1  10
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6,438