Structuring Rule Sets Using Binary Decision Diagrams

Over the years we have seen considerable progress in learning rule-based theories. However, all state-of-the-art rule learners still learn descriptions that directly relate the input features to the target concept and are not able to discover intermediate concepts which might result in a more compact and interpretable theory. An analogous observation can also be made in electronic design automation where the task is to find the minimal representation of a Boolean function: if the representation is not limited to two levels, even smaller circuits can be found. In this paper, we consider binary classification tasks as multi-level logic optimization problems. We take DNF descriptions of the positive class, as obtained by state-of-the-art rule learners, and generate binary decision diagrams with the equivalent expression as the rule set. Finally, a new rule-based theory is extracted from the BDD, which includes new intermediate concepts and is therefore better structured than the original DNF rule set. First experiments on small artificial datasets indicate that intermediate concepts can be reliably detected, and the size of the resulting representations can be compressed, but a first study on a simple real-world dataset showed that the found structures are too complex to be interpretable.