Shifting: One-inclusion mistake bounds and sample compression

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; ≤ d - 1)) / ((n; ≤ d)) < d, which positively resolves a conjecture of Kuzmin and Warmuth relating to their unlabeled Peeling compression scheme and also leads to an improved one-inclusi..