Bootstrap-based criteria for identifying differences between learned Bayesian networks

Bayesian networks provide a powerful framework for learning dependencies from data, and they are widely used to probe structure in biological systems. Biological systems are governed by complex networks of interactions, and uncovering these interactions and comparing them across conditions is central to understanding biological mechanisms. However, when comparing Bayesian networks, it can be difficult to determine whether observed differences are substantial enough to reflect genuine differences in the underlying systems generating the data. Here, we address this by developing bootstrap-based criteria for identifying such differences and demonstrate their performance using simulated data from synthetic Bayesian networks. Both edge-level and whole-network connectivity comparisons reliably identified when underlying networks differed, even when this involved only 5% of edges, while distinguishing these differences from sampling variation. However, even with large datasets, the criteria were unable to recover specific edge differences. Thus distinguishing that networks differed was possible, but not the specific ways they differed. These criteria establish a framework for more robust and standardised Bayesian network comparisons, with broad potential for real-world applications.