Bootstrap re-sampling for unbalanced data in supervised learning

This paper presents a technical framework to assess the impact of re-sampling on the ability of a supervised learning to correctly learn a classification problem. We use the bootstrap expression of the prediction error to identify the optimal re-sampling proportions in binary classification experiments using artificial neural networks. Based on Bayes decision rule and the a priori distribution of the objective data, an estimate for the optimal re-sampling proportion is derived as well as upper and lower bounds for the exact optimal proportion. The analytical considerations to extend the present method to cross-validation and multiple classes are also illustrated. (C) 2001 Elsevier Science B.V. All rights reserved.