Reproduce “Foundations of Structural Causal Models with Latent Selection” on OpenResearch

About this paper

Leihao Chen, Onno Zoeter, Joris M. Mooij

This paper establishes a rigorous theoretical foundation for modeling latent selection bias within Structural Causal Models (SCMs). It introduces a novel conditioning operation to transform SCMs with selection mechanisms into standard SCMs, preserving causal semantics for selected subpopulations and extending graphical representations to include latent selection.

Key insights

• The proposed conditioning operation for SCMs faithfully preserves potential outcome distributions for non-selection variables in the selected subpopulation, allowing for valid causal inference despite latent selection.
• Bidirected edges in Directed Mixed Graphs can serve as a unified graphical representation for non-causal dependencies arising from both latent common causes and latent selection bias.
• The SCM conditioning operation commutes with both marginalization and interventions on variables that are not ancestors of the selection set, providing flexibility and consistency in applying abstraction techniques.

Summary by alphaXiv.