FORESTS OF PROBABILITY ESTIMATION TREES

Abstract

Probability estimation trees (PETs) generalize classification trees in that they assign class probability distributions instead of class labels to examples that are to be classified. This property has been demonstrated to allow PETs to outperform classification trees with respect to ranking performance, as measured by the area under the ROC curve (AUC). It has further been shown that the use of probability correction improves the performance of PETs. This has lead to the use of probability correction also in forests of PETs. However, it was recently observed that probability correction may in fact deteriorate performance of forests of PETs. A more detailed study of the phenomenon is presented and the reasons behind this observation are analyzed. An empirical investigation is presented, comparing forests of classification trees to forests of both corrected and uncorrected PETS on 34 data sets from the UCI repository. The experiment shows that a small forest (10 trees) of probability corrected PETs gives a higher AUC than a similar-sized forest of classification trees, hence providing evidence in favor of using forests of probability corrected PETs. However, the picture changes when increasing the forest size, as the AUC is no longer improved by probability correction. For accuracy and squared error of predicted class probabilities (Brier score), probability correction even leads to a negative effect. An analysis of the mean squared error of the trees in the forests and their variance, shows that although probability correction results in trees that are more correct on average, the variance is reduced at the same time, leading to an overall loss of performance for larger forests. The main conclusions are that probability correction should only be employed in small forests of PETs, and that for larger forests, classification trees and PETs are equally good alternatives.