Identifying Macro Causal Effects in C-DMGs over DMGs
底层有向混合图上的簇图：聚合层面因果效应识别AI 解读 ↓
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底层有向混合图上的簇图：聚合层面因果效应识别
- 研究问题
- 当底层因果结构允许循环、变量被聚合为簇时，do 演算能否完整识别簇层面的因果效应及其不可识别情形？
- 方法与思路
- 作者在允许循环的输入输出结构因果模型下，研究底层有向混合图上的簇图，并分析 do 演算和图形判据。
- 材料陈述的贡献
- 摘要称 do 演算在该图类上具有无条件的可靠性与完备性，并将既有不可识别判据扩展至其中一部分图。
- 阅读关注点
- 应核对无条件所指的限制、循环模型与簇效应的定义，以及完备性定理和不可识别判据各自覆盖的图类。
- 阅读边界
- 这是预印本，同行评审或期刊接收未核实；摘要未展示模型定义及证明，此处宏观指聚合层次，不能解读为宏观经济效应。
原文摘要
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.