Improved Information Gain Estimates for Decision Tree Induction

Ensembles of classification and regression trees remain popular machine learning methods because they define flexible nonparametric models that predict well and are computationally efficient both during training and testing. During induction of decision trees one aims to find predicates that are maximally informative about the prediction target. To select good predicates most approaches estimate an informationtheoretic scoring function, the information gain, both for classification and regression problems. We point out that the common estimation procedures are biased and show that by replacing them with improved estimators of the discrete and the differential entropy we can obtain better decision trees. In effect our modifications yield improved predictive performance and are simple to implement in any decision tree code.