Keep the Decision Tree and Estimate the Class Probabilities Using its Decision Boundary

Isabelle Alvarez, Stephan Bernard, Guillaume Deffuant.

This paper proposes a new method to estimate the class membership probability of the cases classified by a Decision Tree. This method provides smooth class probabilities estimate, without any modification of the tree, when the data are numerical. It applies a posteriori and doesn't use additional training cases. It relies on the distance to the decision boundary induced by the decision tree. The distance is computed on the training sample. It is then used as an input for a very simple one-dimension kernel-based density estimator, which provides an estimate of the class membership probability. This geometric method gives good results even with pruned trees, so the intelligibility of the tree is fully preserved.