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Abstract: We generalize Sauer's Lemma to finite V C-dimension classes functions on [n] = . . . , n} which have a margin of at least N on every element in a sample S [n] of cardinality l, where the margin h (x) of h on a point [n] is defined as the largest non-negative integer a such that h is constant on the interval I a (x) = [x a, x + a]. (Update)
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BibTeX entry: (Update)
J. Ratsaby. A constrained version of sauer's lemma. In Third Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, Vienna, Austria, September 2004 (MathInfo 2004), Proceedings. Birkhuser, 2004. http://citeseer.ist.psu.edu/ratsaby04constrained.html More
@misc{ ratsaby04constrained,
author = "J. Ratsaby",
title = "A constrained version of sauer's lemma",
text = "J. Ratsaby. A constrained version of sauer's lemma. In Third Colloquium
on Mathematics and Computer Science Algorithms, Trees, Combinatorics and
Probabilities, Vienna, Austria, September 2004 (MathInfo 2004), Proceedings.
Birkhuser, 2004.",
year = "2004",
url = "citeseer.ist.psu.edu/ratsaby04constrained.html" }
Citations (may not include all citations):947 Statistical Learning Theory (context) - Vapnik - 1998
454 the uniform convergence of relative frequencies of events to.. (context) - Vapnik, Chervonenkis - 1971
143 An Introduction to Support Vector Machines and other Kernel-.. (context) - Cristianini, Shawe-Taylor - 2000
115 the density of families of sets (context) - Sauer - 1972
114 The Theory of Partitions (context) - Andrews - 1998
88 Neural Network Learning:Theoretical Foundations (context) - Anthony, Bartlett - 1999
21 A generalization of Sauer's Lemma (context) - Haussler, Long - 1995
2 A Sharp Threshold Result for Finite-VC Classes of Large-Marg.. (context) - Ratsaby - 2004
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