An Explicit VC-Theorem for Low-Degree Polynomials

@article{Chattopadhyay2012AnEV,
  title={An Explicit VC-Theorem for Low-Degree Polynomials},
  author={Eshan Chattopadhyay and Adam R. Klivans and Pravesh Kothari},
  journal={Electron. Colloquium Comput. Complex.},
  year={2012},
  volume={19},
  pages={127}
}
Let X ⊆ R n and let \({\cal C}\) be a class of functions mapping ℝ n → { − 1,1}. The famous VC-Theorem states that a random subset S of X of size \(O(\frac{d}{\epsilon^{2}} \log \frac{d}{\epsilon})\), where d is the VC-Dimension of \({\cal C}\), is (with constant probability) an e-approximation for \({\cal C}\) 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 \({\cal C… 
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