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Small weak epsilonnets
, 2008
"... Given a set P of points in the plane, a set of points Q is a weak εnet with respect to a family of sets S (e.g., rectangles, disks, or convex sets) if every set of S containing εP  points contains a point of Q. In this paper, we determine bounds on εS i, the smallest epsilon that can be guarante ..."
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Cited by 13 (1 self)
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Given a set P of points in the plane, a set of points Q is a weak εnet with respect to a family of sets S (e.g., rectangles, disks, or convex sets) if every set of S containing εP  points contains a point of Q. In this paper, we determine bounds on εS i, the smallest epsilon that can
Small weak epsilonnets in three dimensions
 In Proceedings of the 18th Canadian Conference on Computational Geometry
, 2006
"... We study the problem of finding small weak εnets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak εnet of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R3. 1 ..."
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Cited by 5 (0 self)
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We study the problem of finding small weak εnets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak εnet of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R3. 1
Small Weak EpsilonNets in Three Dimensions
"... We study the problem of finding small weak εnets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak εnet of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R 3. 1 ..."
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We study the problem of finding small weak εnets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak εnet of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R 3. 1
New Constructions of Weak EpsilonNets
 In Proc. 19th Annual ACM Symposium on Computational Geometry
, 2003
"... A nite set N R is a weak "net for an npoint set X R (with respect to convex sets) if N intersects every convex set K with jK \ X j "n. We give an alternative, and arguably simpler, proof of the fact, rst shown by Chazelle et al. [8], that every point set X in R admits a ..."
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Cited by 5 (0 self)
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A nite set N R is a weak "net for an npoint set X R (with respect to convex sets) if N intersects every convex set K with jK \ X j "n. We give an alternative, and arguably simpler, proof of the fact, rst shown by Chazelle et al. [8], that every point set X in R admits a
New constructions of weak epsilonnets
 In Proc. 19th Annual ACM Symposium on Computational Geometry
, 2003
"... A finite set N ⊂ R d is a weak εnet for an npoint set X ⊂ R d (with respect to convex sets) if N intersects every convex set K with K ∩ X  ≥ εn. We give an alternative, and arguably simpler, proof of the fact, first shown by Chazelle et al. [8], that every point set X in R d admits a weak εnet ..."
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Cited by 3 (0 self)
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A finite set N ⊂ R d is a weak εnet for an npoint set X ⊂ R d (with respect to convex sets) if N intersects every convex set K with K ∩ X  ≥ εn. We give an alternative, and arguably simpler, proof of the fact, first shown by Chazelle et al. [8], that every point set X in R d admits a weak εnet
Lower bounds for weak epsilonnets and stairconvexity
 IN: PROC. 25TH ACM SYMPOS. COMPUT. GEOM. (SOCG 2009
, 2009
"... A set N ⊂ Rd is called a weak εnet (with respect to convex sets) for a finite X ⊂ Rd if N intersects every convex set C with X ∩ C  ≥ εX. For every fixed d ≥ 2 and every r ≥ 1 we construct sets X ⊂ Rd for which every weak 1 rnet has at least Ω(r logd−1 r) points; this is the first superlinear ..."
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Cited by 13 (5 self)
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A set N ⊂ Rd is called a weak εnet (with respect to convex sets) for a finite X ⊂ Rd if N intersects every convex set C with X ∩ C  ≥ εX. For every fixed d ≥ 2 and every r ≥ 1 we construct sets X ⊂ Rd for which every weak 1 rnet has at least Ω(r logd−1 r) points; this is the first
The strength of weak learnability
 Machine Learning
, 1990
"... Abstract. This paper addresses the problem of improving the accuracy of an hypothesis output by a learning algorithm in the distributionfree (PAC) learning model. A concept class is learnable (or strongly learnable) if, given access to a Source of examples of the unknown concept, the learner with h ..."
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Cited by 861 (24 self)
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with high probability is able to output an hypothesis that is correct on all but an arbitrarily small fraction of the instances. The concept class is weakly learnable if the learner can produce an hypothesis that performs only slightly better than random guessing. In this paper, it is shown that these two
Tight Lower Bounds for the Size of EpsilonNets
"... According to a well known theorem of Haussler and Welzl (1987), any range space of bounded VCdimension admits an εnet of size O () ..."
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Cited by 22 (1 self)
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According to a well known theorem of Haussler and Welzl (1987), any range space of bounded VCdimension admits an εnet of size O ()
Boosting a Weak Learning Algorithm By Majority
, 1995
"... We present an algorithm for improving the accuracy of algorithms for learning binary concepts. The improvement is achieved by combining a large number of hypotheses, each of which is generated by training the given learning algorithm on a different set of examples. Our algorithm is based on ideas pr ..."
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Cited by 516 (15 self)
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presented by Schapire in his paper "The strength of weak learnability", and represents an improvement over his results. The analysis of our algorithm provides general upper bounds on the resources required for learning in Valiant's polynomial PAC learning framework, which are the best general
Results 1  10
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1,536,042