Finding Probabilistic Rule Lists using the Minimum Description Length Principle

An important task in data mining is that of rule discovery in supervised data. Well-known examples include rule-based classification and subgroup discovery. Motivated by the need to succinctly describe an entire labeled dataset, rather than accurately classify the label, we propose an MDL-based supervised rule discovery task. The task concerns the discovery of a small rule list where each rule captures the probability of the Boolean target attribute being true. Our approach is built on a novel combination of two main building blocks: (i) the use of the Minimum Description Length (MDL) principle to characterize good-and- small sets of probabilistic rules, (ii) the use of branch-and-bound with a best-first search strategy to find better-than-greedy and optimal solutions for the proposed task. We experimentally show the effectiveness of our approach, by providing a comparison with other supervised rule learning algorithms on real-life datasets