  Bayesian networks faithfully represent the symmetric conditional
independences existing between the components of a random vector. Staged trees
are an extension of Bayesian networks for categorical random vectors whose
graph represents non-symmetric conditional independences via vertex coloring.
However, since they are based on a tree representation of the sample space, the
underlying graph becomes cluttered and difficult to visualize as the number of
variables increases. Here we introduce the first structural learning algorithms
for the class of simple staged trees, entertaining a compact coalescence of the
underlying tree from which non-symmetric independences can be easily read. We
show that data-learned simple staged trees often outperform Bayesian networks
in model fit and illustrate how the coalesced graph is used to identify
non-symmetric conditional independences.
