Efficient Estimation of Generalization Error and Bias-Variance Components of Ensembles

For many applications, an ensemble of base classifiers is an effective solution. The tuning of its parameters (number of classifiers, amount of data on which each classifier is to be trained on, etc.) requires G, the generalization error of a given ensemble. The efficient estimation of G is the focus of this paper. The key idea is to approximate the variance of the class scores/probabilities of the base classifiers over the randomness imposed by the training subset by normal/beta distribution at each point x in the input feature space. We estimate the parameters of the distribution using a small set of randomly chosen base classifiers and use those parameters to give efficient estimation schemes for G. We give empirical evidence for the quality of the various estimators. We also demonstrate their usefulness in making design choices such as the number of classifiers in the ensemble and the size of subset of data used for training that are needed to achieve a certain value of generalization error. Our approach also has great potential for designing distributed ensemble classifiers.