Optimizing Binary Decision Diagrams for Interpretable Machine Learning Classification

Machine learning (ML) is ever more frequently used as a tool to aid decision making. The need to understand the decisions made by ML algorithms has sparked a renewed interest in explainable ML models. A number of known models are often regarded as interpretable by human decision makers with varying degrees of difficulty. The size of such models plays a crucial role in determining how easily they can be understood by a human. In this article we propose the use of binary decision diagrams (BDDs) as an interpretable ML model. BDDs can be deemed as interpretable as decision trees (DTs) while offering a often more compact representation due to node sharing. Fixed variable ordering also allows for more concise explanations. We propose a SAT-based approach for learning optimal BDDs that exhibit perfect accuracy on training data. We also explore heuristic methods for computing suboptimal BDDs, in order to improve scalability. We also investigate procedures to transform instances of known ML models into BDDs in order to provide more concise explanations.