The VC-Dimension of Axis-Parallel Boxes on the Torus

preprint2020arXivOpen access

We show in this paper that the VC-dimension of the family of $d$ -dimensional axis-parallel boxes and cubes on the $d$ -dimensional torus are both asymptotically $d \log_2(d)$ . This is especially surprising as the VC-dimension usually grows linearly with $d$ in similar settings.

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The VC-Dimension of Axis-Parallel Boxes on the Torus

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