Out-of-bag estimation of the optimal sample size in bagging

The performance of mm-out-of-nn bagging with and without replacement in terms of the sampling ratio (m/n)(m/n) is analyzed. Standard bagging uses resampling with replacement to generate bootstrap samples of equal size as the original training set mwor=nmwor=n. Without-replacement methods typically use half samples mwr=n/2mwr=n/2. These choices of sampling sizes are arbitrary and need not be optimal in terms of the classification performance of the ensemble. We propose to use the out-of-bag estimates of the generalization accuracy to select a near-optimal value for the sampling ratio. Ensembles of classifiers trained on independent samples whose size is such that the out-of-bag error of the ensemble is as low as possible generally improve the performance of standard bagging and can be efficiently built.