Adjustment Identification Distance: A gadjid for Causal Structure
  Learning
Leonard Henckel Theo Würtzen Sebastian Weichwald
Evaluating graphs learned by causal discovery algorithms is difficult: The
number of edges that differ between two graphs does not reflect how the graphs
differ with respect to the identifying formulas they suggest for causal
effects. We introduce a framework for developing causal distances between
graphs which includes the structural intervention distance for directed acyclic
graphs as a special case. We use this framework to develop improved
adjustment-based distances as well as extensions to completed partially
directed acyclic graphs and causal orders. We develop polynomial-time
reachability algorithms to compute the distances efficiently. In our package
gadjid (open source at https://github.com/CausalDisco/gadjid), we provide
implementations of our distances; they are orders of magnitude faster than the
structural intervention distance and thereby provide a success metric for
causal discovery that scales to graph sizes that were previously prohibitive.