Unlabeled Compression Schemes Exceeding the VC-dimension

11/29/2018

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by   Dömötör Pálvölgyi, et al.

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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.