Corpus ID: 237485165

Littlestone and VC-dimension of families of zero sets

@inproceedings{Guingona2021LittlestoneAV,
  title={Littlestone and VC-dimension of families of zero sets},
  author={Vincent Guingona and Alexei D. Kolesnikov and Julie Nierwinski and Richard Soucy},
  year={2021}
}
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. 

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