An Ensemble of Optimal Trees for Class Membership Probability Estimation

Machine learning methods can be used for estimating the class membership probability of an observation. We propose an ensemble of optimal trees in terms of their predictive performance. This ensemble is formed by selecting the best trees from a large initial set of trees grown by random forest. A proportion of trees is selected on the basis of their individual predictive performance on out-of-bag observations. The selected trees are further assessed for their collective performance on an independent training data set. This is done by adding the trees one by one starting from the highest predictive tree. A tree is selected for the final ensemble if it increases the predictive performance of the previously combined trees. The proposed method is compared with probability estimation tree, random forest and node harvest on a number of bench mark problems using Brier score as a performance measure. In addition to reducing the number of trees in the ensemble, our method gives better results in most of the cases. The results are supported by a simulation study.