Work

Distinguishability of causal structures under latent confounding and selection

Year: 2026

Type: article

Abstract: Statistical relationships in observed data can arise for several different reasons: the observed variables may be causally related, they may share a latent common cause, or there may be selection bias. Each of these scenarios can be modelled using different causal graphs. Not all such causal graphs, however, can be distinguished by experimental data. In this paper, we formulate the equivalence class of causal graphs as a novel graphical structure, the selected-marginalized directed graph (smDG). That is, we show that two directed acyclic graphs with latent and selected vertices have the same smDG if and only if they are indistinguishable, even when allowing for arbitrary interventions on the observed variables. As a substitute for the more familiar d -separation criterion for DAGs, we provide an analogous sound and complete separation criterion in smDGs for conditional independence relative to passive observations. Finally, we provide a series of sufficient conditions under which two causal structures are indistinguishable when there is only access to passive observations.

Source: Journal of Causal Inference

DOI: 10.1515/jci-2025-0067

Authors: Ryan Carey, Marina Maciel Ansanelli, Elie Wolfe, Robin J. Evans

Institutions: University of Oxford, University of Waterloo, Perimeter Institute

Language: English

Topic: Bayesian Modeling and Causal Inference

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,187