An Optimization Approach to Learning Falling Rule Lists

A falling rule list is a probabilistic decision list for binary classification, consisting of a series of if-then rules with antecedents in the if clauses and probabilities of the desired outcome ("1") in the then clauses. Just as in a regular decision list, the order of rules in a falling rule list is important -- each example is classified by the first rule whose antecedent it satisfies. Unlike a regular decision list, a falling rule list requires the probabilities of the desired outcome ("1") to be monotonically decreasing down the list. We propose an optimization approach to learning falling rule lists and "softly" falling rule lists, along with Monte-Carlo search algorithms that use bounds on the optimal solution to prune the search space.