Sphere Packing Numbers for Subsets of the Boolean n-Cube with Bounded Vapnik-Chervonenkis Dimension

@article{Haussler1995SpherePN,
  title={Sphere Packing Numbers for Subsets of the Boolean n-Cube with Bounded Vapnik-Chervonenkis Dimension},
  author={D. Haussler},
  journal={J. Comb. Theory, Ser. A},
  year={1995},
  volume={69},
  pages={217-232}
}
  • D. Haussler
  • Published 1995
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
Let V contained in {0,1}^n have Vapnk-Chervonenkis dimension d. Let M(k/n,V) denote the cardinality of the largest W contained in V such that any two distinct vectors in W differ on at least k indices. We show that M(k/n,V) >= (cn/(k+d))^d for some constant c. This improves on the previous best result of ((cn/k)log(n/k))^d. This new result has applications in the theory of empirical processes. 
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