  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.
