Learning Large Bayesian Networks with Expert Constraints

Abstract

We propose a new score-based algorithm for learning the structure of a Bayesian Network (BN). It is the first algorithm that simultaneously supports the requirements of (i) learning a BN of bounded treewidth, (ii) satisfying expert constraints, including positive and negative ancestry properties between nodes, and (iii) scaling up to BNs with several thousand nodes. The algorithm operates in two phases. In Phase 1, we utilize a modified version of an existing BN structure learning algorithm, modified to generate an initial Directed Acyclic Graph (DAG) that supports a portion of the given constraints. In Phase 2, we follow the BN-SLIM framework, introduced by Peruvemba Ramaswamy and Szeider (AAAI 2021). We improve the initial DAG by repeatedly running a MaxSAT solver on selected local parts. The MaxSAT encoding entails local versions of the expert constraints as hard constraints. We evaluate a prototype implementation of our algorithm on several standard benchmark sets. The encouraging results demonstrate the power and flexibility of the BN-SLIM framework. It boosts the score while increasing the number of satisfied expert constraints.