The Upper and Lower Bounds of the Prediction Accuracies of Ensemble Methods for Binary Classification

Ensemble methods have been widely used to improve prediction accuracy over individual classifiers. In this paper, we achieve a few results about the prediction accuracies of ensemble methods for binary classification that are missed or misinterpreted in previous literature. First we show the upper and lower bounds of the prediction accuracies (i.e. the best and worst possible prediction accuracies) of ensemble methods. Next we show that an ensemble method can achieve > 0.5 prediction accuracy, while individual classifiers have < 0.5 prediction accuracies. Furthermore, for individual classifiers with different prediction accuracies, the average of the individual accuracies determines the upper and lower bounds. We perform two experiments to verify the results and show that it is hard to achieve the upper and lower bounds accuracies by random individual classifiers and better algorithms need to be developed.