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Ample completions of OMs and CUOMs (2007.12527v2)
Published 24 Jul 2020 in math.CO and cs.DM
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.