Identifying Macro Causal Effects in C-DMGs over DMGs

• URL: http://arxiv.org/abs/2506.19650v1
• Date: Tue, 24 Jun 2025 14:14:43 GMT
• Title: Identifying Macro Causal Effects in C-DMGs over DMGs
• Authors: Simon Ferreira, Charles K. Assaad,
• Abstract summary: We prove that the do-calculus is unconditionally sound and complete for identifying macro causal effects in C-DMGs over DMGs.<n>ioSCMs induce another type of graph structure known as a directed mixed graph (DMG)<n>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.
• Score: 0.9208007322096533
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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