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VCdimension and shortest path algorithms
"... We explore the relationship between VCdimension and graph algorithm design. In particular, we show that set systems induced by sets of vertices on shortest paths have VCdimension at most two. This allows us to use a result from learning theory to improve time bounds on query algorithms for the p ..."
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Cited by 17 (5 self)
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We explore the relationship between VCdimension and graph algorithm design. In particular, we show that set systems induced by sets of vertices on shortest paths have VCdimension at most two. This allows us to use a result from learning theory to improve time bounds on query algorithms
Cluster Ensembles  A Knowledge Reuse Framework for Combining Multiple Partitions
 Journal of Machine Learning Research
, 2002
"... This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse&ap ..."
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Cited by 603 (20 self)
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This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse
Hitting sets when the VCdimension is small
, 2004
"... We present an approximation algorithm for the hitting set problem when the VCdimension of the set system is small. Our algorithm builds on Pach & Agarwal [7], and we show how it can be parallelized and extended to the minimum cost hitting set problem. The running time of the proposed algorithm ..."
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We present an approximation algorithm for the hitting set problem when the VCdimension of the set system is small. Our algorithm builds on Pach & Agarwal [7], and we show how it can be parallelized and extended to the minimum cost hitting set problem. The running time of the proposed algorithm
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
Popper, Falsification and the VCdimension
, 2005
"... We compare Sir Karl Popper’s ideas concerning the falsifiability of a theory with similar notions from VCtheory. Having located some divergences, we discuss how best to view Popper’s work from the perspective of statistical learning theory. ..."
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Cited by 1 (0 self)
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We compare Sir Karl Popper’s ideas concerning the falsifiability of a theory with similar notions from VCtheory. Having located some divergences, we discuss how best to view Popper’s work from the perspective of statistical learning theory.
VCDimension of Exterior Visibility of Polyhedra
, 2001
"... In this paper, we address the problem of finding the minimal number of viewpoints outside a polyhedron in two or three dimensions such that every point on the exterior of the polyhedron is visible from at least one of the chosen viewpoints. This problem which we call the minimum fortress guard probl ..."
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Cited by 3 (2 self)
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this problem shows the NPcompleteness of MFGP. Instead of relying on heuristic searches, we address the approximability of the camera placement problem. It is well known (and easy to see) that this problem can be cast as a hitting set problem. While the approximability of generic instances of the hitting set
Calculating the VCDimension of Decision Trees
"... Abstract—We propose an exhaustive search algorithm that calculates the VCdimension of univariate decision trees with binary features. The VCdimension of the univariate decision tree with binary features depends on (i) the VCdimension values of the left and right subtrees, (ii) the number of input ..."
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Cited by 2 (0 self)
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of inputs, and (iii) the number of nodes in the tree. From a training set of example trees whose VCdimensions are calculated by exhaustive search, we fit a general regressor to estimate the VCdimension of any binary tree. These VCdimension estimates are then used to get VCgeneralization bounds
VCdimensions of random function classes
 DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 2007
"... For any class of binary functions on [n] = {1,..., n} a classical result by Sauer states a sufficient condition for its VCdimension to be at least d: its cardinality should be at least O(n d−1). A necessary condition is that its cardinality be at least 2 d (which is O(1) with respect to n). How do ..."
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Cited by 2 (2 self)
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is still significantly smaller than the sufficient size of O(n d−1)) then it shatters every set of size d with high probability. The behavior in the neighborhood of these thresholds is described by the asymptotic probability distribution of the VCdimension and of the largest d such that all sets of size d
Measuring The VCdimension Using Optimized Experimental Design
 Neural Computation
, 1969
"... VCdimension is the measure of model complexity (capacity) used in VCtheory. The knowledge of the VCdimension of an estima 2 tor is necessary for rigorous complexity control using analytic VC generalization bounds. Unfortunately, it is not possible to obtain the analytic estimates of the VCd ..."
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Cited by 19 (1 self)
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in most cases. Hence, it has been recently proposed to measure the VCdimension of an estimator experimentally by fitting the theoretical formula to a set of experimental measurements of the frequency of errors on artificially generated data sets of varying sizes (Vapnik et al, 1994). However, it may
Results 1  10
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