Unlabeled Compression Schemes Exceeding the VC-dimension
This addresses a theoretical problem in machine learning for researchers in computational learning theory, providing a counterexample to a known conjecture.
The paper disproves a conjecture by Kuzmin and Warmuth that every family with VC-dimension at most d has an unlabeled compression scheme of size at most d, and it studies joins of families to propose a larger gap between VC-dimension and compression scheme size.
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.