Information fusion between knowledge and data in Bayesian network structure learning

Bayesian Networks (BNs) have become a powerful technology for reasoning under uncertainty, particularly in areas that require causal assumptions that enable us to simulate the effect of intervention. The graphical structure of these models can be determined by causal knowledge, learnt from data, or a combination of both. While it seems plausible that the best approach in constructing a causal graph involves combining knowledge with machine learning, this approach remains underused in practice. We implement and evaluate 10 knowledge approaches with application to different case studies and BN structure learning algorithms available in the open-source Bayesys structure learning system. The approaches enable us to specify pre-existing knowledge that can be obtained from heterogeneous sources, to constrain or guide structure learning. Each approach is assessed in terms of structure learning effectiveness and efficiency, including graphical accuracy, model fitting, complexity, and runtime; making this the first paper that provides a comparative evaluation of a wide range of knowledge approaches for BN structure learning. Because the value of knowledge depends on what data are available, we illustrate the results both with limited and big data. While the overall results show that knowledge becomes less important with big data due to higher learning accuracy rendering knowledge less important, some of the knowledge approaches are actually found to be more important with big data. Amongst the main conclusions is the observation that reduced search space obtained from knowledge does not always imply reduced computational complexity, perhaps because the relationships implied by the data and knowledge are in tension.