Introduction: Learn One Rule does not employ a test set when evaluating rules. Assessments of rule quality as described above are made with tuples from the original training data.
Such assessment is optimistic because the rules will likely over fit the data. That is, the rules may perform well on the training data, but less well on subsequent data. To compensate for this, we can prune the rules. A rule is pruned by removing a conjunct (attribute test). We choose to prune a rule, R, if the pruned version of R has greater quality, as assessed on an independent set of tuples. As in decision tree pruning, we refer to this set as a pruning set. Various pruning strategies can be used, such as the pessimistic pruning approach described in the previous section. FOIL uses a simple yet effective method. Given a rule, R,
FOIL_Prune(R) = pos-neg / pos neg
where pos and neg are the number of positive and negative tuples covered by R, respectively. This value will increase with the accuracy of R on a pruning set. Therefore, if the FOIL Prune value is higher for the pruned version of R, then we prune R. By convention, RIPPER starts with the most recently added conjunct when considering pruning. Conjuncts are pruned one at a time as long as this results in an improvement.
