Expectation maximization based ordering aggregation for improving the K2 structure learning algorithm

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.