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. BN structure learning (BNSL) from multiscale biomedical data is a central problem in this context. Computational methods for BNSL inherit the limitations of the underlying BN model selection criteria. As a result, quantification of model features, structural consistency, and interpretability are often suboptimal, making data-driven BNSL context-dependent and unstable, and leading to BNs that are not directly comparable across studies. The recently introduced Minimum Uncertainty (MU) model selection principle aims to mitigate some of these concerns. However, the applicability range, statistical calibration, and empirical operating characteristics of the corresponding criterion remain to be addressed. Here, we derive a new calibrated MU criterion under broad perturbation assumptions and develop a dedicated statistical relationship model for assessing the operating characteristics of BN scoring criteria via misclassification error assessment. This framework enables systematic evaluation of sensitivity, specificity, and robustness behavior across parameter regimes and dependence modes. We validate the findings numerically and demonstrate performance gains on real biomedical data. Results The new MU criterion is robust across a wide range of parameters and consistently outperforms the other criteria considered. It overcomes the sensitivity degradation frequently seen with conventional scores, improves results consistency and generalizability, and delivers the interpretability needed for cross-application use. The accompanying statistical model further enhances interpretability by enabling accuracy and power estimates for individual dependencies, thereby providing a calibrated empirical framework for both evaluating the recovered BN models in practical applications and comparing BN scoring criteria in general. Conclusions Beyond the new MU criterion itself, this work establishes a general statistical framework for evaluating score-based BNSL in terms of empirical operating characteristics, including at a single-edge level. The resulting methodology improves the reliability, comparability, and practical interpretability of reconstructed BNs across diverse biomedical research scenarios.