Automated construction of an Object-Oriented Bayesian Network (OOBN) Class Hierarchy

Bayesian networks (BNs) are a widely used probabilistic modelling tool for reasoning under uncertainty, though scaling them up for complex real-world problems can be challenging. Object-Oriented Bayesian Networks (OOBNs) have been proposed to address this challenge, providing modellers with the ability to define hierarchies of classes and use these classes to construct models with a compositional and hierarchical structure, enabling reuse and supporting maintenance. The object-oriented concept of inheritance supports reuse of existing components, but comes with the challenge of building, and then maintaining, an efficient hierarchy of classes. This paper proposes a supergraph based method that constructs class inheritance hierarchies from a set of OOBN classes; this can be used either to form an initial inheritance hierarchy, or to reform an existing hierarchy into a more efficient one. We also present heuristics to convert a BN to an OOBN class, measures to evaluate a constructed hierarchy and empirical analyses of the proposed approach on synthetic hierarchies and on a real-world OOBN project; results show the algorithm works well in practice.

I. Introduction

Bayesian networks (BNs) [1] are a powerful and widely used tool for reasoning under uncertainty. They can be built by automated learning if data is available [2] or using elicitation methods to capture expert knowledge when it is not. Especially when most or all of the model is built by-hand, BN modelling methods don't scale up well; the resultant large complex BNs are difficult to visualise and hard for the domain experts and decision-makers to understand, reducing the acceptance and subsequent use of the model. Researchers have tried to address this issue by dividing the problem into sub-parts and then combining the BN models for the sub-problems, and by reusing with some modifications BN models previously built and validated for another application. These techniques include object-oriented BNs (OOBNs) [3], probabilistic relational models (PRM) and plate models, OOPRM, generalised decision-graphs, BN fragments, varieties combining PRM and objects, such as module networks, multi-entity BNs (MEBNs), idioms, and template-based representations.