Optimizing Binary Decision Diagrams for Interpretable Machine Learning Classification
Gianpiero Cabodi1,a, Paolo E. Camurati1,b, Alexey Ignatiev2, Joao Marques-Silva3, Marco Palena1,c and Paolo Pasini1,d
1DAUIN, Politecnico di Torino, Turin, IT
agianpiero.cabodi@polito.it
bpaolo.camurati@polito.it
cmarco.palena@polito.it
epaolo.pasini@polito.it
2Monash University, Melbourne, AU
alexey.ignatiev@monash.edu
3ANITI, University of Toulouse, Toulouse, FR
joao.marques-silva@univ-toulouse.fr
ABSTRACT
Motivated by the need to understand the behaviour of complex machine learning (ML) models, there has been recent interest in learning optimal (or sub-optimal) decision trees (DTs). This interest is explained by the fact that DTs are widely regarded as interpretable by human decision makers. An alternative to DTs are Binary Decision Diagrams (BDDs), which can be deemed interpretable. Compared to DTs, and despite a fixed variable order, BDDs offer the advantage of more compact representations in practice, due to node sharing. Moreover, there is also extensive experience in the efficient manipulation of BDDs. Our work proposes preliminary inroads in two main directions: (a) proposing a SAT-based model for computing a decision tree as the smallest Reduced Ordered Binary Decision Diagram, consistent with given training data; and (b) exploring heuristic approaches for deriving sub-optimal (i.e., not minimal) ROBDDs, in order to improve the scalability of the proposed technique. The heuristic approach is related to recent work on using BDDs for classification. Whereas previous works addressed size reduction by general logic synthesis techniques, our work adds the contribution of generalized cofactors, that are a well-known compaction technique specific to BDDs, once a care (or equivalently a don’t care) set is given. Preliminary experimental results are also provided, proposing a direct comparison between optimal and sub-optimal solutions, as well as an evaluation of the impact of the proposed size reduction steps.
Keywords: Binary Decision Diagrams, SAT, Classification.
