Ample completions of OMs and CUOMs
Combinatorics
2021-09-22 v2 Discrete Mathematics
Abstract
This paper considers completions of COMs (complexes oriented matroids) to ample partial cubes of the same VC-dimension. We show that these exist for OMs (oriented matroids) and CUOMs (complexes of uniform oriented matroids). This implies that OMs and CUOMs satisfy the sample compression conjecture -- one of the central open questions of learning theory. We conjecture that every COM can be completed to an ample partial cube without increasing the VC-dimension.
Keywords
Cite
@article{arxiv.2007.12527,
title = {Ample completions of OMs and CUOMs},
author = {Victor Chepoi and Kolja Knauer and Manon Philibert},
journal= {arXiv preprint arXiv:2007.12527},
year = {2021}
}
Comments
24 pages, 11 figures