  Causal Bayesian networks have become a powerful technology for reasoning
under uncertainty in areas that require transparency and explainability, by
relying on causal assumptions that enable us to simulate hypothetical
interventions. The graphical structure of such models can be estimated by
structure learning algorithms, domain knowledge, or a combination of both.
Various knowledge approaches have been proposed in the literature that enable
us to specify prior knowledge that constrains or guides these algorithms. This
paper introduces some novel, and also describes some existing, knowledge-based
approaches that enable us to combine structure learning with knowledge obtained
from heterogeneous sources. We investigate the impact of these approaches on
structure learning across different algorithms, case studies and settings that
we might encounter in practice. Each approach is assessed in terms of
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 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 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.
