Generalization error of ensemble estimators

It has been empirically shown that a better estimate with less generalization error can be obtained by averaging outputs of multiple estimators. This paper presents an analytical result for the generalization error of ensemble estimators. First, we derive a general expression of the ensemble generalization error by using factors of interest (bias, variance, covariance, and noise variance) and show how the generalization error is affected by each of them. Some special cases are then investigated. The result of a simulation is shown to verify our analytical result. A practically important problem of the ensemble approach, ensemble dilemma, is also discussed.