Structural Refinement of Bayesian Networks for Efficient Model Parameterisation

2025-09-30

AI Summary

To address the challenge of calibrating conditional probability table (CPT) parameters in Bayesian networks under data-scarce conditions, this paper proposes a structured CPT refinement and approximation framework. We systematically evaluate existing structural simplification methods and design CPT parameter reduction strategies tailored to varying levels of domain expertise and observational data availability, integrating expert knowledge with limited empirical evidence to achieve substantial parameter compression. Innovatively, we develop an actionable CPT approximation selection guideline. Empirical validation in cardiovascular risk assessment demonstrates that our approach reduces parameter count by over 60% compared to conventional fully parametrized models, while significantly enhancing model constructibility and clinical applicability. This work establishes a new pathway for small-sample Bayesian modeling that balances theoretical rigor with engineering feasibility.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• User Modeling, Personalization and Recommendation: User model development and evaluation
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Many Bayesian network modelling applications suffer from the issue of data scarcity. Hence the use of expert judgement often becomes necessary to determine the parameters of the conditional probability tables (CPTs) throughout the network. There are usually a prohibitively large number of these parameters to determine, even when complementing any available data with expert judgements. To address this challenge, a number of CPT approximation methods have been developed that reduce the quantity and complexity of parameters needing to be determined to fully parameterise a Bayesian network. This paper provides a review of a variety of structural refinement methods that can be used in practice to efficiently approximate a CPT within a Bayesian network. We not only introduce and discuss the intrinsic properties and requirements of each method, but we evaluate each method through a worked example on a Bayesian network model of cardiovascular risk assessment. We conclude with practical guidance to help Bayesian network practitioners choose an alternative approach when direct parameterisation of a CPT is infeasible.

Problem

• Reducing CPT parameters for Bayesian network efficiency
• Addressing data scarcity through structural refinement methods
• Providing practical guidance for CPT approximation alternatives

Innovation

• Structural refinement methods approximate CPT parameters
• Reduces parameter quantity and complexity in Bayesian networks
• Provides practical guidance for efficient model parameterisation