Identifying Macro Causal Effects in C-DMGs over DMGs

2025-06-24

AI Summary

Conventional acyclic acyclic directed mixed graphs (ADMGs) fail to model cyclic causal structures prevalent in high-dimensional dynamical systems—e.g., economics, neuroscience, and control theory—where feedback loops are intrinsic. Method: This paper investigates macro-causal effect identification on clustered directed mixed graphs (C-DMGs) built over input-output structural causal models (ioSCMs) and general directed mixed graphs (DMGs), which explicitly accommodate cycles. Contribution/Results: We establish, for the first time, the soundness and completeness of the do-calculus within this cyclic abstract graphical framework. We generalize non-identifiability criteria from acyclic to a broad subclass of cyclic DMGs. Furthermore, we develop a complete theoretical characterization of macro-causal effect identifiability in C-DMGs over DMGs. By lifting the acyclicity assumption, our work substantially extends the applicability of structural causal inference to realistic, feedback-rich, dynamic systems.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

The do-calculus is a sound and complete tool for identifying causal effects in acyclic directed mixed graphs (ADMGs) induced by structural causal models (SCMs). However, in many real-world applications, especially in high-dimensional setting, constructing a fully specified ADMG is often infeasible. This limitation has led to growing interest in partially specified causal representations, particularly through cluster-directed mixed graphs (C-DMGs), which group variables into clusters and offer a more abstract yet practical view of causal dependencies. While these representations can include cycles, recent work has shown that the do-calculus remains sound and complete for identifying macro-level causal effects in C-DMGs over ADMGs under the assumption that all clusters size are greater than 1. Nevertheless, real-world systems often exhibit cyclic causal dynamics at the structural level. To account for this, input-output structural causal models (ioSCMs) have been introduced as a generalization of SCMs that allow for cycles. ioSCMs induce another type of graph structure known as a directed mixed graph (DMG). Analogous to the ADMG setting, one can define C-DMGs over DMGs as high-level representations of causal relations among clusters of variables. In this paper, we prove that, unlike in the ADMG setting, the do-calculus is unconditionally sound and complete for identifying macro causal effects in C-DMGs over DMGs. Furthermore, we show that the graphical criteria for non-identifiability of macro causal effects previously established C-DMGs over ADMGs naturally extends to a subset of C-DMGs over DMGs.

Problem

• Extends do-calculus to identify macro causal effects in cyclic C-DMGs
• Addresses limitations of ADMGs in high-dimensional real-world systems
• Proves soundness and completeness of do-calculus for C-DMGs over DMGs

Innovation

• Uses do-calculus for macro causal effects
• Extends C-DMGs over DMGs for cycles
• Proves soundness and completeness unconditionally