Threshold functions for Extension Statements
Journal of Combinatorial Theory Series A
Decision theoretic generalizations of the PAC model for neural net and other learning applications
Information and Computation
The Vapnik-Chervonenkis dimension of a random graph
Selected papers of the 14th British conference on Combinatorial conference
The nature of statistical learning theory
The nature of statistical learning theory
The phase transition in a random hypergraph
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
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A set of vertices is shattered in a hypergraph if any of its subsets is obtained as the intersection of an edge with the set. The VC dimension is the size of the largest shattered subset. Under the binomial model of k-uniform random hypergraphs, the threshold function for the VC dimension to be larger than a given integer is obtained. The same is done for the testing dimension, which is the largest integer d such that all sets of cardinality d are shattered. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007