Accurate Robust and Efficient Error Estimation for Decision Trees

This paper illustrates a novel approach to the estimation of generalization error of decision tree classifiers. We set out the study of decision tree errors in the context of consistency analysis theory, which proved that the Bayes error can be achieved only if when the number of data samples thrown into each leaf node goes to infinity. For the more challenging and practical case where the sample size is finite or small, a novel sampling error term is introduced in this paper to cope with the small sample problem effectively and efficiently. Extensive experimental results show that the proposed error estimate is superior to the well-known K-fold cross validation methods in terms of robustness and accuracy. Moreover it is orders of magnitudes more efficient than cross validation methods.