Interpretable Causal Graphical Models for Equilibrium Systems with Confounding

2026-03-25

AI Summary

This work addresses the challenge of causal inference in equilibrium systems confounded by latent variables, where interpretable graphical modeling approaches have been lacking. It introduces antorial graphs into the causal modeling of equilibrium systems for the first time, integrating counterfactual graphs with the Single-World Intervention Graph (SWIG) framework to construct a unified, interpretable causal diagram that jointly represents both observed and counterfactual variables. The proposed method not only yields a clear graphical representation of confounded equilibrium systems but also enables on-demand construction of covariate adjustment sets, offering element-wise flexibility to selectively include or exclude specific variables. This fine-grained control facilitates valid and efficient identification of causal effects under complex equilibrium conditions.

Technology Category

Reasoning under Uncertainty: CausalityMachine Learning: Causal LearningKnowledge Representation and Reasoning: Action, Change, and Causality

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingResponsible Web: Algorithmic accountability and transparency on the web

Abstract

In applications, quantities of interest are often modelled in equilibrium or an equilibrium solution is sought. The presence of confounding makes causal inference in this setting challenging. We provide interpretable graphical models for equilibrium systems with confounding using anterial graphs (Lauritzen and Sadeghi, 2018), a class of graphs containing directed acyclic graphs, ancestral graphs, and chain graphs. In this setting, we provide valid graphical representations of both counterfactual variables and observational variables, which we relate to counterfactual graphs (Shpitser and Pearl, 2007) and single-world intervention graphs (Richardson and Robins,2013). As an application of this graphical representation, we provide an element-wise procedure of selecting adjustment sets that flexibly include and exclude given covariates.

Problem

• causal inference
• equilibrium systems
• confounding
• graphical models
• counterfactuals

Innovation

• antorial graphs
• equilibrium systems
• confounding
• causal graphical models
• adjustment set selection