  Causal discovery algorithms aim at untangling complex causal relationships
from data. Here, we study causal discovery and inference methods based on
staged tree models, which can represent complex and asymmetric causal
relationships between categorical variables. We provide a first graphical
representation of the equivalence class of a staged tree, by looking only at a
specific subset of its underlying independences. We further define a new
pre-metric, inspired by the widely used structural intervention distance, to
quantify the closeness between two staged trees in terms of their corresponding
causal inference statements. A simulation study highlights the efficacy of
staged trees in uncovering complexes, asymmetric causal relationships from
data, and real-world data applications illustrate their use in practical causal
analysis.
