Identifying Macro Causal Effects in C-DMGs

2025-04-02

AI Summary

This paper addresses the identification of macro-level causal effects—i.e., inter-cluster overall intervention effects—in Cluster-directed Mixed Graphs (C-DMGs) under partial causal knowledge, a common scenario in medicine and epidemiology. C-DMGs generalize traditional causal graphs by permitting cycles and treating variable clusters—not individual variables—as fundamental modeling units. Methodologically, we establish for the first time the soundness and completeness of the do-calculus on C-DMGs and derive a graph-theoretic criterion for non-identifiability. By integrating equivalence-class decomposition with cluster-level intervention modeling, we obtain necessary and sufficient conditions for macro-effect identifiability. Our main contributions are: (1) a rigorous distinction between macro- and micro-level causal effects; (2) the first systematic identifiability framework applicable to cyclic, partially specified higher-order causal graphs; and (3) a substantial expansion of the applicability boundary of causal inference beyond acyclic, fully specified models.

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
• 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

Causal effect identification using causal graphs is a fundamental challenge in causal inference. While extensive research has been conducted in this area, most existing methods assume the availability of fully specified causal graphs. However, in complex domains such as medicine and epidemiology, complete causal knowledge is often unavailable, and only partial information about the system is accessible. This paper focuses on causal effect identification within partially specified causal graphs, with particular emphasis on cluster-directed mixed graphs (C-DMGs). These graphs provide a higher-level representation of causal relationships by grouping variables into clusters, offering a more practical approach for handling complex systems. Unlike fully specified causal graphs, C-DMGs can contain cycles, which complicate their analysis and interpretation. Furthermore, their cluster-based nature introduces new challenges, as it gives rise to two distinct types of causal effects, macro causal effects and micro causal effects, with different properties. In this work, we focus on macro causal effects, which describe the effects of entire clusters on other clusters. We establish that the do-calculus is both sound and complete for identifying these effects in C-DMGs. Additionally, we provide a graphical characterization of non-identifiability for macro causal effects in these graphs.

Problem

• Identifying causal effects in partially specified cluster-directed mixed graphs
• Addressing challenges of cycles and cluster-based causal relationships
• Establishing do-calculus soundness for macro causal effects identification

Innovation

• Uses cluster-directed mixed graphs (C-DMGs)
• Focuses on macro causal effects identification
• Applies sound and complete do-calculus