The VC-Dimension of Axis-Parallel Boxes on the Torus
- URL: http://arxiv.org/abs/2004.13861v1
- Date: Tue, 28 Apr 2020 21:41:05 GMT
- Title: The VC-Dimension of Axis-Parallel Boxes on the Torus
- Abstract summary: We show that the VC-dimension of the family of $d$-dimensional axis, boxes and cubes are bothparallelally $d log_2(d)$.
This is especially surprising as the VC-dimension usually grows linearly with $d$ in similar settings.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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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