  Causal machine learning (ML) algorithms recover graphical structures that
tell us something about cause-and-effect relationships. The causal
representation praovided by these algorithms enables transparency and
explainability, which is necessary for decision making in critical real-world
problems. Yet, causal ML has had limited impact in practice compared to
associational ML. This paper investigates the challenges of causal ML with
application to COVID-19 UK pandemic data. We collate data from various public
sources and investigate what the various structure learning algorithms learn
from these data. We explore the impact of different data formats on algorithms
spanning different classes of learning, and assess the results produced by each
algorithm, and groups of algorithms, in terms of graphical structure, model
dimensionality, sensitivity analysis, confounding variables, predictive and
interventional inference. We use these results to highlight open problems in
causal structure learning and directions for future research. To facilitate
future work, we make all graphs, models, data sets, and source code publicly
available online.
