Adjustment Identification Distance: A gadjid for Causal Structure Learning
This work addresses the challenge of accurately assessing causal structure learning for researchers in causal inference, though it is incremental as it builds on existing distance metrics.
The paper tackles the problem of evaluating causal discovery algorithms by introducing a framework for causal distances between graphs, which includes improved adjustment-based distances and efficient algorithms. The result is an open-source package, gadjid, that computes these distances orders of magnitude faster than previous methods, enabling scalability to previously prohibitive graph sizes.
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 new reachability algorithms to compute the distances efficiently and to prove their low polynomial time complexity. In our package gadjid (open source at https://github.com/CausalDisco/gadjid), we provide implementations of our distances; they are orders of magnitude faster with proven lower time complexity than the structural intervention distance and thereby provide a success metric for causal discovery that scales to graph sizes that were previously prohibitive.