Generalizing Labeled and Unlabeled Sample Compression to Multi-label Concept Classes

Rahim Samei, Boting Yang, Sandra Zilles

Abstract: This paper studies sample compression of maximum multi-label concept classes for various notions of VC-dimension. It formulates a sufficient condition for a notion of VC-dimension to yield labeled compression schemes for maximum classes of dimension d in which the compression sets have size at most d. The same condition also yields a so-called tight sample compression scheme, which we define to generalize Kuzmin and Warmuth’s unlabeled binary scheme to the multi-label case. The well-known Graph dimension satisfies our sufficient condition, while neither Pollard’s pseudo-dimension nor the Natarajan dimension does.