Learning Optimal Decision Sets and Lists with SAT

Abstract

Decision sets and decision lists are two of the most easily explainable machine learning models. Given the renewed emphasis on explainable machine learning decisions, both of these machine learning models are becoming increasingly attractive, as they combine small size and clear explainability. In this paper, we define size as the total number of literals in the SAT encoding of these rule-based models as opposed to earlier work that concentrates on the number of rules. In this paper, we develop approaches to computing minimum-size “perfect” decision sets and decision lists, which are perfectly accurate on the training data, and minimal in size, making use of modern SAT solving technology. We also provide a new method for determining optimal sparse alternatives, which trade off size and accuracy. The experiments in this paper demonstrate that the optimal decision sets computed by the SAT-based approach are comparable with the best heuristic methods, but much more succinct, and thus, more explainable. We contrast the size and test accuracy of optimal decisions lists versus optimal decision sets, as well as other state-of-the-art methods for determining optimal decision lists. Finally, we examine the size of average explanations generated by decision sets and decision lists.