Predictive Ensemble Pruning by Expectation Propagation

Abstract—An ensemble is a group of learners that work together as a committee to solve a problem. The existing ensemble learning algorithms often generate unnecessarily large ensembles, which consume extra computational resource and may degrade the generalization performance. Ensemble pruning algorithms aim to find a good subset of ensemble members to constitute a small ensemble, which saves the computational resource and performs as well as, or better than, the unpruned ensemble. This paper introduces a probabilistic ensemble pruning algorithm by choosing a set of “sparse ” combination weights, most of which are zeros, to prune the ensemble. In order to obtain the set of sparse combination weights and satisfy the non-negative constraint of the combination weights, a left-truncated, non-negative, Gaussian prior is adopted over every combination weight. Expectation propagation (EP) algorithm is employed to approximate the posterior estimation of the weight vector. The leave-one-out (LOO) error can be obtained as a byproduct in the training of EP without extra computation and is a good indication for the generalization error. Therefore, the LOO error is used together with the Bayesian evidence for model selection in this algorithm. An empirical study on several regression and classification benchmark data sets shows that our algorithm utilizes far less component learners but performs as well as, or better than, the unpruned ensemble. Our results are very competitive compared with other ensemble pruning algorithms. Index Terms—Machine learning, Probabilistic algorithms