Structural Intervention Distance for Evaluating Causal Graphs
Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-)metric between DAGs, the structural intervention distance (SID). The SID is based on a graphical criterion only and quantifies the closeness between two DAGs in terms of their corresponding causal inference statements. It is therefore well suited
... efore well suited for evaluating graphs that are used for computing interventions. Instead of DAGs, it is also possible to compare CPDAGs, completed partially DAGs that represent Markov equivalence classes. The SID differs significantly from the widely used structural Hamming distance and therefore constitutes a valuable additional measure. We discuss properties of this distance and provide a (reasonably) efficient implementation with software code available on the first author's home page. distribution by L(X) and denote corresponding densities of L(X) with respect to Lebesgue or the counting measure, by p(·) (implicitly assuming their existence). We also denote conditional densities and the density of L(Z) with Z ⊂ X by p(·). A graph G = (V, E ) consists of nodes V and edges E ⊆ V × V. With a slight abuse of notation, we sometimes identify the nodes (or vertices) j ∈ V with the variables X j .