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328
VC Dimension in Circuit Complexity
 In Proceedings of the 11th Annual IEEE Conference on Computational Complexity CCC'96
, 1995
"... The main result of this paper is a \Omega\Gamma n 1=4 ) lower bound on the size of a sigmoidal circuit computing a specific AC 0 2 function. This is the first lower bound for the computation model of sigmoidal circuits with unbounded weights. We also give upper and lower bounds for the same funct ..."
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Cited by 6 (1 self)
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). When OE is the sign function H, the threshold circuit model is recovered. Of particular int...
VC Dimension in Circuit Complexity
 In Proceedings of the 11th Annual IEEE Conference on Computational Complexity CCC'96
, 1995
"... The main result of this paper is a \Omega\Gamma n 1=4 ) lower bound on the size of a sigmoidal circuit computing a specific AC 0 2 function. This is the first lower bound for the computation model of sigmoidal circuits with unbounded weights. We also give upper and lower bounds for the same funct ..."
Abstract
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). When OE is the sign function H , the threshold circuit model is recovered. Of particular inte...
The VC dimension of constraintbased grammars
, 2009
"... We analyze the complexity of Harmonic Grammar (HG), a linguistic model in which licit underlyingtosurfaceform mappings are determined by optimization over weighted constraints. We show that the VapnikChervonenkis Dimension of HG grammars with k constraints is k − 1. This establishes a fundamental ..."
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Cited by 4 (1 self)
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fundamental bound on the complexity of HG in terms of its capacity to classify sets of linguistic data that has significant ramifications for learnability. The VC dimension of HG is the same as that of Optimality Theory (OT), which is similar to HG, but uses ranked rather than weighted constraints
The VC dimension of constraintbased grammars
"... We analyze the complexity of Harmonic Grammar (HG), a linguistic model in which licit underlyingtosurfaceform mappings are determined by optimization over weighted constraints. We show that the VapnikChervonenkis Dimension of HG grammars with k constraints is k − 1. This establishes a fundamental ..."
Abstract
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fundamental bound on the complexity of HG in terms of its capacity to classify sets of linguistic data that has significant ramifications for learnability. The VC dimension of HG is the same as that of Optimality Theory (OT), which is similar to HG, but uses ranked rather than weighted constraints
Lower bounds for evolution strategies using VCdimension
 PARALLEL PROBLEM SOLVING FROM NATURE, DORTMUND: GERMANY (2008)
, 2008
"... We derive lower bounds for comparisonbased or selectionbased algorithms, improving existing results in the continuous setting, and extending them to nontrivial results in the discrete case. We introduce for that the use of the VCdimension of the level sets of the fitness functions; results are t ..."
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Cited by 12 (5 self)
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We derive lower bounds for comparisonbased or selectionbased algorithms, improving existing results in the continuous setting, and extending them to nontrivial results in the discrete case. We introduce for that the use of the VCdimension of the level sets of the fitness functions; results
Lower Bounds for Comparison Based Evolution Strategies using VCdimension and Sign Patterns
 ALGORITHMICA
, 2010
"... We derive lower bounds on the convergence rate of comparison based or selection based algorithms, improving existing results in the continuous setting, and extending them to nontrivial results in the discrete case. This is achieved by considering the VCdimension of the level sets of the fitness fu ..."
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Cited by 10 (3 self)
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We derive lower bounds on the convergence rate of comparison based or selection based algorithms, improving existing results in the continuous setting, and extending them to nontrivial results in the discrete case. This is achieved by considering the VCdimension of the level sets of the fitness
Generalizing univariate signed rank statistics for testing and estimating a multivariate location parameter
, 1993
"... Abstract. We generalize signed rank statistics to dimensions higher than one. This results in a class of orthogonally invariant and distribution free tests that can be used for testing spherical symmetry/location parameter. The corresponding estimator is orthogonally equivariant. Both the test and e ..."
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Cited by 27 (4 self)
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Abstract. We generalize signed rank statistics to dimensions higher than one. This results in a class of orthogonally invariant and distribution free tests that can be used for testing spherical symmetry/location parameter. The corresponding estimator is orthogonally equivariant. Both the test
Learnability of Bipartite Ranking Functions
 PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON LEARNING THEORY
, 2005
"... The problem of ranking, in which the goal is to learn a realvalued ranking function that induces a ranking or ordering over an instance space, has recently gained attention in machine learning. We define a model of learnability for ranking functions in a particular setting of the ranking problem k ..."
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Cited by 12 (2 self)
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ranking function class in the same way as do the standard VCdimension related shatter coefficients (growth function) for classes of classification functions, do not grow too quickly. Our second main result gives a necessary condition for learnability: we define a new combinatorial parameter for a class
Comparisons of Generalized rank tests versus Multivariate Rank Tests for Microarray Data
"... In this talk, we compare the performances of two types of nonparametric tests, the generalized rank tests and multivariate rank tests, in testing for dierentially expressed genes between experimental conditions based on replicated microarray experiments. Lee et al. (2004) generalized the Wilcoxon r ..."
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ranksum test and signedrank test to include replications. The multivariate rank tests introduced by Puri and Sen (1971) rank replicates separately, and then construct a quadratic test statistics to incorporate correlations among dierent replicates. These two types of rankbased tests may have
Results 1  10
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328