In this note we disprove a conjecture of Kuzmin and Warmuth claiming that every family whose VC-dimension is at most d admits an unlabeled compression scheme to a sample of size at most d. We also study the unlabeled compression schemes of the joins of some families and conjecture that these give a larger gap between the VC-dimension and the size of the smallest unlabeled compression scheme for them.
- Compression schemes
- Learning theory
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics