On the Generalization of the C-Bound to Multiclass Setting

PAC-Bayesian theory provides generalization bounds for weighted majority vote. However, these bounds do not directly focus on the risk of the majority vote, but on the risk of the Gibbs classifier. Indeed, it is well-known that the Gibbs classifier and the majority vote are related. To the best of our knowledge the tightest relation is the C-bound proposed by Lacasse et al. (2007); Laviolette et al. (2011) for binary classification. In this paper, we provide three generalizations of the C-bound to multiclass setting