Quantifying uncertainty in Bayesian Networks structural learning

The key goals in learning Bayesian networks (BNs) from data are to identify significant statistical relationships between variables and to build a Directed Acyclic Graph (DAG) that represents these relationships through Joint Probability Distributions. Most research relies on score-based or conditional test methods for model selection. However, when using real-world data, it can be challenging to identify whether the learned DAG represents the underlying relations inherent in the limited datasets, particularly when evaluating data obtained from multiple independent sources. This study presents a methodology to assess the credible interval for both the existence and direction of each edge within Bayesian networks derived from data. Furthermore, it explores the fusion of models acquired from distinct and independent datasets. This approach enables the Bayesian learning of Bayesian Networks (BNs) from data by treating the uncertainty associated with the existence and orientation of each edge as a random variable. By evaluating the probability of the orientation of each edge, it is possible to suggest the existence of a potential latent variable within the dataset. If an edge exhibits equiprobable directions and is verified to exist, it becomes a plausible hypothesis for a latent variable. The Fast Causal Algorithm, originally introduced by 1, is the foundation of this approach. Finally, by employing a maximum a posteriori estimation, the most prominent edges and their respective orientations are identified and employed to create the leading DAG. We present our findings in simulated datasets with different length sizes. By comparing the structure of the learned DAGs with existing structures and evaluating the inference capabilities of the final BN, we establish that our approach achieves results comparable to the most recent studies in the field, while offering insights into the model's reliability and improving the use of the data.