Example of learning a Bayesian network using expert knowledge

H. Amirkhani, M. Rahmati, P. J. F. Lucas and A. Hommersom, Exploiting Experts’ Knowledge for Structure Learning of Bayesian Networks, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 39, no. 11, pp. 2154-2170, DOI: 10.1109/TPAMI.2016.2636828.

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.

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