Shifting: One-inclusion mistake bounds and sample compression

  • Authors:

  • Benjamin I. P. Rubinstein;Peter L. Bartlett;J. Hyam Rubinstein

  • Affiliations:

  • Computer Science Division, University of California, Berkeley, 387 Soda Hall #1776, Berkeley, CA 94720-1776, USA;Computer Science Division, University of California, Berkeley, 387 Soda Hall #1776, Berkeley, CA 94720-1776, USA and Department of Statistics, University of California, Berkeley, 367 Evans Hall #3 ...;Department of Mathematics & Statistics, the University of Melbourne, Parkville, VIC 3010, Australia

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2009

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Abstract

We present new expected risk bounds for binary and multiclass prediction, and resolve several recent conjectures on sample compressibility due to Kuzmin and Warmuth. By exploiting the combinatorial structure of concept class F, Haussler et al. achieved a VC(F)/n bound for the natural one-inclusion prediction strategy. The key step in their proof is a d=VC(F) bound on the graph density of a subgraph of the hypercube-one-inclusion graph. The first main result of this paper is a density bound of n(n-1=