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VC Dimension
, 2008
"... VC dimension (for Vapnik Chervonenkis dimension) measures the capacity of a hypothesis space. Capacity is a measure of complexity and measures the expressive power, richness or flexibility of a set of functions by assessing how wiggly its members can be. The definitions below are taken from Vapnik ( ..."
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VC dimension (for Vapnik Chervonenkis dimension) measures the capacity of a hypothesis space. Capacity is a measure of complexity and measures the expressive power, richness or flexibility of a set of functions by assessing how wiggly its members can be. The definitions below are taken from Vapnik
VCDimension of Rule Sets
"... Abstract—In this paper, we give and prove lower bounds of the VCdimension of the rule set hypothesis class where the input features are binary or continuous. The VCdimension of the rule set depends on the VCdimension values of its rules and the number of inputs. Index Terms—VCDimension, Rule set ..."
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Abstract—In this paper, we give and prove lower bounds of the VCdimension of the rule set hypothesis class where the input features are binary or continuous. The VCdimension of the rule set depends on the VCdimension values of its rules and the number of inputs. Index Terms—VCDimension, Rule
Classification with infinite VCdimension
"... Families of finite VCdimension are not able of ensuring a good asymptotic behavior for any distribution. We sum up and compare paradigms for working without finiteness of the VCdimension and compare them. ..."
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Families of finite VCdimension are not able of ensuring a good asymptotic behavior for any distribution. We sum up and compare paradigms for working without finiteness of the VCdimension and compare them.
VC Dimension of Neural Networks
 Neural Networks and Machine Learning
, 1998
"... . This paper presents a brief introduction to VapnikChervonenkis (VC) dimension, a quantity which characterizes the difficulty of distributionindependent learning. The paper establishes various elementary results, and discusses how to estimate the VC dimension in several examples of interest in ne ..."
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Cited by 24 (3 self)
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. This paper presents a brief introduction to VapnikChervonenkis (VC) dimension, a quantity which characterizes the difficulty of distributionindependent learning. The paper establishes various elementary results, and discusses how to estimate the VC dimension in several examples of interest
VCdimension of Exterior Visibility
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2004
"... In this paper, we study the VapnikChervonenkis (VC)dimension of set systems arising in 2D polygonal and 3D polyhedral configurations where a subset consists of all points visible from one camera. In the past, it has been shown that the VCdimension of planar visibility systems is bounded by 23 if t ..."
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Cited by 13 (1 self)
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In this paper, we study the VapnikChervonenkis (VC)dimension of set systems arising in 2D polygonal and 3D polyhedral configurations where a subset consists of all points visible from one camera. In the past, it has been shown that the VCdimension of planar visibility systems is bounded by 23
VCdimension of visibility on terrains
 In Proc. 20th Canadian Conference on Comput. Geom
, 2008
"... A guarding problem can naturally be modeled as a set system (U, S) in which the universe U of elements is the set of points we need to guard and our collection S of sets contains, for each potential guard g, the set of points from U seen by g. We prove bounds on the maximum VCdimension of set syste ..."
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Cited by 2 (0 self)
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A guarding problem can naturally be modeled as a set system (U, S) in which the universe U of elements is the set of points we need to guard and our collection S of sets contains, for each potential guard g, the set of points from U seen by g. We prove bounds on the maximum VCdimension of set
VCDimension of Sets of Permutations
 Combinatorica
, 2000
"... We define the VCdimension of a set of permutations A ae S n to be the maximal k such that there exist distinct i 1 ; :::; i k 2 f1; :::; ng that appear in A in all possible linear orders, that is, every linear order of fi 1 ; :::; i k g is equivalent to the standard order of f(i 1 ); :::; (i k )g ..."
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Cited by 6 (0 self)
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We define the VCdimension of a set of permutations A ae S n to be the maximal k such that there exist distinct i 1 ; :::; i k 2 f1; :::; ng that appear in A in all possible linear orders, that is, every linear order of fi 1 ; :::; i k g is equivalent to the standard order of f(i 1 ); :::; (i k
VCDimensions For Graphs
, 1994
"... We study set systems over the vertex set (or edge set) of some graph that are induced by special graph properties like clique, connectedness, path, star, tree, etc. We derive a variety of combinatorial and computational results on the VC (VapnikChervonenkis) dimension of these set systems. For most ..."
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Cited by 1 (0 self)
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We study set systems over the vertex set (or edge set) of some graph that are induced by special graph properties like clique, connectedness, path, star, tree, etc. We derive a variety of combinatorial and computational results on the VC (VapnikChervonenkis) dimension of these set systems
On the VCDimension of the Choquet Integral
"... Abstract. The idea of using the Choquet integral as an aggregation operator in machine learning has gained increasing attention in recent years, and a number of corresponding methods have already been proposed. Complementing these contributions from a more theoretical perspective, this paper address ..."
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addresses the following question: What is the VC dimension of the (discrete) Choquet integral when being used as a binary classifier? The VC dimension is a key notion in statistical learning theory and plays an important role in estimating the generalization performance of a learning method. Although we
On the complexity of approximating the vc dimension
 J. Comput. Syst. Sci
, 2001
"... We study the complexity of approximating the VC dimension of a collection of sets, when the sets are encoded succinctly by a small circuit. We show that this problem is • Σ p 3hard to approximate to within a factor 2 − ɛ for any ɛ> 0, • approximable in AM to within a factor 2, and • AMhard to a ..."
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Cited by 20 (3 self)
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We study the complexity of approximating the VC dimension of a collection of sets, when the sets are encoded succinctly by a small circuit. We show that this problem is • Σ p 3hard to approximate to within a factor 2 − ɛ for any ɛ> 0, • approximable in AM to within a factor 2, and • AM
Results 1  10
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