Littlestone and VC-dimension of families of zero sets

Vincent Guingona; Alexei Kolesnikov; Julie Nierwinski; Richard Soucy

Littlestone and VC-dimension of families of zero sets

Logic 2021-09-13 v1

Authors: Vincent Guingona , Alexei Kolesnikov , Julie Nierwinski , Richard Soucy

Abstract

We prove that, for any $d$ linearly independent functions from some set into a $d$ -dimensional vector space over any field, the family of zero sets of all non-trivial linear combination of these functions has VC-dimension and Littlestone dimension $d-1$ . Additionally, we characterize when such families are maximal of VC-dimension $d-1$ and give a sufficient condition for when they are maximal of Littlestone dimension $d-1$ .

Keywords

VC-dimension Littlestone dimension zero sets linearly independent functions maximal families

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@article{arxiv.2109.04805,
  title  = {Littlestone and VC-dimension of families of zero sets},
  author = {Vincent Guingona and Alexei Kolesnikov and Julie Nierwinski and Richard Soucy},
  journal= {arXiv preprint arXiv:2109.04805},
  year   = {2021}
}

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18 pages

Littlestone and VC-dimension of families of zero sets

Abstract

Keywords

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