Boosting in PN Spaces

This paper analyzes boosting in unscaled versions of ROC spaces, also referred to as PN spaces. A minor revision to AdaBoost’s reweighting strategy is analyzed, which allows to reformulate it in terms of stratification, and to visualize the boosting process in nested PN spaces as known from divide-and-conquer rule learning. The analyzed confidence-rated algorithm is proven to take more advantage of its base models in each iteration, although also searching a space of linear discrete base classifier combinations. The algorithm reduces the training error quicker without lacking any of the advantages of original AdaBoost. The PN space interpretation allows to derive a lower-bound for the area under the ROC curve metric (AUC) of resulting ensembles based on the AUC after reweighting. The theoretical findings of this paper are complemented by an empirical evaluation on benchmark datasets.