Efficient and accurate structural fusion of Bayesian networks

Abstract

Bayesian Network (BN) fusion provides a precise theoretical framework for aggregating the graphical structure of a set of BNs into a consensus network. The fusion process depends on a total ordering of the variables, but both the problem of searching for an optimal consensus structure (according to the standard problem definition) as well as the one of looking for the optimal ordering are NP-hard.In this paper we start with this theoretical framework and extend it from a practical point of view. The two main methodological contributions we make are: (1) an adaptation of the well-known BN learning algorithm GES (Greedy Equivalence Search) to the case of having a set of BNs as input instead of data (we prove the correctness of the adapted algorithm, i.e., under certain standard assumptions the optimal solution for the BN fusion process is obtained); and (2) a heuristic method for identifying a suitable order of the variables, which allows us to obtain consensus BNs having (far) fewer edges than those obtained by using random orderings.Finally, we design several computational experiments to test our proposals. From the results, we can conclude that the consensus network can be efficiently obtained by using the proposed heuristic to compute the total order of the variables, with this DAG being very close to the optimal one.