Distinguishability of causal structures under latent confounding and selection

2025-09-24

AI Summary

This paper addresses the observational indistinguishability of causal structures under concurrent latent confounding and selection bias. We propose the selection-marginally directed graph (smDG) as a unifying representation framework, providing the first systematic characterization of equivalence classes of causal graphs accommodating both latent variables and selection bias. Building upon a generalized notion of d-separation, we establish a conditional independence separation criterion for passive observational data, fully characterizing interventionally indistinguishable causal structures. Our method integrates causal graph theory with conditional independence testing to construct the first causal inference framework specifically designed for settings with dual biases. We formally prove the completeness and correctness of smDGs in preserving equivalence across arbitrary interventions, and derive a sufficient condition system for indistinguishability—thereby significantly expanding the identifiability boundary of causal discovery.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• Web Mining and Content Analysis: Bridging structured and unstructured data

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.

Problem

• Distinguishing causal structures under latent confounding and selection bias
• Formulating equivalence classes using selected-marginalized directed graphs
• Providing separation criteria for conditional independence in observational data

Innovation

• Introduces selected-marginalized directed graph structure
• Provides separation criterion for conditional independence
• Establishes conditions for indistinguishable causal structures