Formal analysis of cross-validation for rule induction using probabilistic indices

This paper proposes a new framework for evaluation of cross-validation methods for rule induction based on statistical indices by using incremental sampling scheme. Although incremental sampling scheme is used for incremental rule induction, this paper shows that the same idea can be used for deletion of exampling, called decremental sampling scheme. Then, we applied this technique to the cross-validation method for rules define by the propositions whose constraints were define by inequalities of accuracy and coverage. The results show that the evaluation framework gives a powerful tool for evaluation of cross-validation.