How do some Bayesian Network machine learned graphs compare to causal knowledge?

The graph of a BN can be machine learned, determined by causal knowledge, or a combination of both. In disciplines like bioinformatics, applying BN structure learning algorithms can reveal new insights that would otherwise remain unknown. However, these algorithms are less effective when the input data are limited in terms of sample size, which is often the case when working with real data. This paper focuses on purely machine learned and purely knowledge-based BNs and investigates their differences in terms of graphical structure and how well the implied statistical models explain the data. The tests are based on four previous case studies that had their BN structure determined by domain knowledge. Using various metrics, we compare the knowledge-based graphs to the machine learned graphs generated from various algorithms implemented in TETRAD spanning all three classes of learning. The results show that while the algorithms are much better at arriving at a graph with a high model selection score, the parameterised models obtained from those graphs tend to be poor predictors of variables of interest, relative to the corresponding inferences obtained from the knowledge-based graphs. Amongst our conclusions is that structure learning is ineffective in the presence of limited sample size relative to model dimensionality, which can be explained by model fitting becoming increasingly distorted under these conditions; essentially rendering ground truth graphs inaccurate by guiding algorithms towards graphical patterns that may share higher evaluation scores and yet deviate further from the ground truth graph. This highlights the value of causal knowledge in these cases, as well as the need for more appropriate model selection scores. Lastly, the experiments also provide new evidence that support the notion that results from simulated data tell us little about actual real-world performance.