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An Explicit VC-Theorem for Low-Degree Polynomials
[chapter]

2012
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Lecture Notes in Computer Science
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Let X ⊆ R n and let C be a class of functions mapping R n → {−1, 1}. The famous VC-Theorem states that a random subset S of X of size O( d ǫ 2 log d ǫ ), where d is the VC-Dimension of C, is (with constant probability) an ǫ-approximation for C with respect to the uniform distribution on X. In this work, we revisit the problem of constructing S explicitly. We show that for any X ⊆ R n and any Boolean function class C that is uniformly approximated by degree k, low-weight polynomials, an

doi:10.1007/978-3-642-32512-0_42
fatcat:qef3ghouf5dihm6ttda42b7efe