Reliable Bayesian Network Structure Learning in Biomedical Applications: Model Uncertainty Criterion and Its Operating Characteristics.

Background: Bayesian network (BN) modeling and computational systems biology have a long history of productive synergy. Learning BN structure from multiscale biomedical data is a central problem in this context. Computational methods for model reconstruction inherit the limitations of the underlying model selection criteria. As a result, the quantification of model features, structural consistency, and interpretability can suffer, making data-driven BNs context-dependent, unstable, and not directly portable across studies. Some of these concerns have been addressed by the introduction of the Minimum model Uncertainty (MU) principle and the corresponding MU scoring criterion. This work develops and refines the MU criterion, comprehensively assessing its operating characteristics in comparison with conventional scoring criteria to ensure its wide applicability across diverse biomedical research scenarios. Methods: The MU criterion is derived under broad network neighborhood considerations. Quality is assessed using misclassification error estimates. To enable this, we construct a dedicated statistical relationship model. We validate the findings numerically and demonstrate performance gains on real biomedical data. Results: The refined MU criterion is robust across a wide range of parameters and consistently outperforms the other scoring criteria considered, mitigating the sensitivity degradation seen with conventional scores, improving result consistency and generalizability, and delivering the interpretability needed for cross-application use. The accompanying statistical model further enhances interpretability by enabling accuracy/power estimates for individual dependencies.