On the Generalization of the C-Bound to Structured Output Ensemble Methods

Abstract: This paper generalizes an important result from the PAC-Bayesian literature for binary classification to the case of ensemble methods for structured outputs. We prove a generic version of the \Cbound, an upper bound over the risk of models expressed as a weighted majority vote that is based on the first and second statistical moments of the vote's margin. This bound may advantageously $(i)$ be applied on more complex outputs such as multiclass labels and multilabel, and $(ii)$ allow to consider margin relaxations. These results open the way to develop new ensemble methods for structured output prediction with PAC-Bayesian guarantees.