A New Information Measure Based on Example-Dependent Misclassification Costs and Its Application in Decision Tree Learning

Abstract

This article describes how the costs of misclassification given with the individual training objects for classification learning can be used in the construction of decision trees for minimal cost instead of minimal error class decisions. This is demonstrated by defining modified, cost-dependent probabilities, a new, cost-dependent information measure, and using a cost-sensitive extension of the CAL5 algorithm for learning decision trees. The cost-dependent information measure ensures the selection of the (local) next best, that is, cost-minimizing, discriminating attribute in the sequential construction of the classification trees. This is shown to be a cost-dependent generalization of the classical information measure introduced by Shannon, which only depends on classical probabilities. It is therefore of general importance and extends classic information theory, knowledge processing, and cognitive science, since subjective evaluations of decision alternatives can be included in entropy and the transferred information. Decision trees can then be viewed as cost-minimizing decoders for class symbols emitted by a source and coded by feature vectors. Experiments with two artificial datasets and one application example show that this approach is more accurate than a method which uses class dependent costs given by experts a priori.

A Bayes Risk Minimization Machine for Example-Dependent Cost Classification

“…This approximate way of dealing with EDCs suffers the drawbacks of sampling techniques, which can modify the problem by reducing the influence of critical samples and/or emphasizing unimportant instances [20]. Decision trees have also been considered for EDC problems [21], [22], and perceptrons and piecewise linear classifiers were used in [23] with an hybrid learning algorithm that constructs separating hyperplanes for each pair of classes. In general, all these techniques suffer from the limitations of the constrained partition of the input space.…”