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arXiv · 2109.04805

Littlestone and VC-dimension of families of zero sets

Vincent Guingona·Alexei Kolesnikov·Julie Nierwinski·Richard Soucy
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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 $d-1$.

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Vincent Guingona, Alexei Kolesnikov, Julie Nierwinski, Richard Soucy. 2021-09-10. Littlestone and VC-dimension of families of zero sets. https://arxiv.org/abs/2109.04805

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