Levels of Confidence and Utility for Binary Classifiers

Two performance measures for binary tree classifiers are introduced: the level of confidence and the level of utility. Both measures are probabilities of desirable events in the construction process of a classifier and hence are easily and intuitively interpretable. The statistical estimation of these measures is discussed. The usual maximum likelihood estimators are shown to have upward biases, and an entropy-based bias-reducing methodology is proposed. Along the way, the basic question of appropriate sample sizes at tree nodes is considered.