  Ensembles of classification and regression trees remain popular machine
learning methods because they define flexible non-parametric 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 information-theoretic 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.
