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Learning Bayesian network structures from data is known to be hard, mainly because the number of candidate graphs is super-exponential in the number of variables. Furthermore, using observational data alone, the true causal graph is not discernible from other graphs that model the same set of conditional independencies. In this paper, it is investigated whether Bayesian network structure learning can be improved by exploiting the opinions of multiple domain experts regarding cause-effect relationships. In practice, experts have different individual probabilities of correctly labeling the inclusion or exclusion of edges in the structure. The accuracy of each expert is modeled by three parameters. Two new scoring functions are introduced that score each candidate graph based on the data and experts’ opinions, taking into account their accuracy parameters. In the first scoring function, the experts’ accuracies are estimated using an expectation-maximization-based algorithm and the estimated accuracies are explicitly used in the scoring process. The second function marginalizes out the accuracy parameters to obtain more robust scores when it is not possible to obtain a good estimate of experts’ accuracies. The experimental results on simulated and real world datasets show that exploiting experts’ knowledge can improve the structure learning if we take the experts’ accuracies into account. [ABSTRACT FROM AUTHOR]

Some of the basic algorithms for learning the structure of Bayesian networks, such as the well-known K2 algorithm, require a prior ordering over the nodes as part of the input. It is well known that the accuracy of the K2 algorithm is highly sensitive to the initial ordering. In this paper, we introduce the aggregation of ordering information provided by multiple experts to obtain a more robust node ordering. In order to reduce the effect of novice participants, the accuracy of each person is used in the aggregation process. The accuracies of participants, not known in advance, are estimated by the expectation maximization algorithm. Any possible contradictions occurred in the resulting aggregation are resolved by modelling the result as a directed graph and avoiding the cycles in this graph. Finally, the topological order of this graph is used as the initial ordering in the K2 algorithm. The experimental results demonstrate the effectiveness of the proposed method in improving the structure learning process. [ABSTRACT FROM AUTHOR]