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. This paper describes and evaluates a set of information fusion methods that have been implemented in the open-source Bayesys structure learning system. The methods enable users to specify pre-existing knowledge and rule-based information that can be obtained from heterogeneous sources, to constrain or guide structure learning. Each method is assessed in terms of structure learning impact, including graphical accuracy, model fitting, complexity and runtime. The results are illustrated both with limited and big data, with application to three BN structure learning algorithms available in Bayesys, and reveal interesting inconsistencies about their effectiveness where the results obtained from graphical measures often contradict those obtained from model fitting measures. While the overall results show that information fusion methods become less effective with big data due to higher learning accuracy rendering knowledge less important, some information fusion methods do perform better with big data. Lastly, amongst the main conclusions is the observation that reduced search space obtained from knowledge constraints does not imply reduced computational complexity, which can happen when the constraints set up a tension between what the data indicate and what the constraints are trying to enforce.