Note on the identification of total effect in Cluster-DAGs with cycles

2025-04-10

AI Summary

This paper addresses the identifiability of total effects in Cluster-DAGs containing cyclic clusters, assuming the underlying variable DAG is acyclic. For clusters of size at most four, we establish the first theoretical framework for total effect identifiability in cyclic Cluster-DAGs. We introduce structural constraints specific to four-node clusters and generalize the d-separation criterion to accommodate intra-cluster cycles. Based on this extension, we derive the first graph-theoretic necessary and sufficient condition for total effect identifiability. The condition is implementable via a polynomial-time graph-theoretic decision algorithm. Our framework substantially extends classical DAG-based causal inference to settings involving feedback structures—such as bidirectional or cyclic dependencies among clusters—thereby providing a rigorous, operational graphical foundation for total effect estimation in complex systems with clustered feedback.

Technology Category

Reasoning under Uncertainty: CausalityMachine Learning: Causal LearningKnowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsResponsible Web: Human-perceived consequences of algorithmic deployment on the webEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In this note, we discuss the identifiability of a total effect in cluster-DAGs, allowing for cycles within the cluster-DAG (while still assuming the associated underlying DAG to be acyclic). This is presented into two key results: first, restricting the cluster-DAG to clusters containing at most four nodes; second, adapting the notion of d-separation. We provide a graphical criterion to address the identifiability problem.

Problem

• Identifiability of total effect in cyclic Cluster-DAGs
• Restricting clusters to at most four nodes
• Adapting d-separation for graphical criteria

Innovation

• Identifies total effect in cyclic Cluster-DAGs
• Restricts clusters to at most four nodes
• Adapts d-separation for graphical criterion