An analytical threshold for combining Bayesian Networks

Abstract Structural learning of Bayesian Networks (BNs) is an NP-hard problem, and the use of sub-optimal strategies is essential in domains involving many variables. One approach is the generation of multiple approximate structures and then reduce the ensemble to a representative structure. This can be performed by using the occurrence frequency (on the structures ensemble) as the criteria for accepting a dominant directed edge between two nodes and thus obtaining the single structure. In this paper, an analogy with an adapted one-dimensional random-walk was used for analytically deducing an appropriate decision threshold to such occurrence frequency. The obtained closed-form expression has been validated across the synthetic datasets applying the Matthews Correlation Coefficient (MCC) as the performance metric. In the experiments using a recent medical dataset, the resulting BN from the analytical cutoff-frequency captured the expected associations among nodes and also achieved better prediction performance than the BNs learned with neighbours thresholds to the computed.