Conceptual perspectives on defining distances between causal graphs

Conceptual perspectives on defining distances between causal graphs.

Leonard Henckel, University College Dublin.

5th of February 2026

Abstract: 

Causal graphical models are a particularly popular paradigm for causal reasoning. One challenge in working with them is that they often lack well-defined and meaningful distances. This limits our ability to evaluate graph estimators practically, study their theoretical properties or quantify uncertainty in their estimates. Existing measures, such as the structural Hamming distance, are edge-by-edge mismatch counts and thus lack a conceptual grounding in what the graphs represent. In this talk, I discuss two distinct and complementary philosophies for developing more meaningful distances. The first philosophy is what we call model-oriented: it centers the causal models the graphs represent. More concretely, we propose organizing the graphs in a partially ordered set based on model inclusion. The model-oriented distance between two graphs is then defined as the length of the shortest path through neighbors in this partial ordering. This provides an intellectually parsimonious yet elegant way to define meaningful distances across causal graph classes. We also illustrate the framework for several concrete graph classes. The second philosophy is what we call task-oriented: it centers a concrete task we wish to use our causal graphs for and defines distance by the number of errors that would result if one graph were used to solve a task while the true model followed the other graph. Using this framework, we develop several concrete distances for the task of identifying causal effects.