提出图形判据，让复杂因果图可简化为易懂的前门调整形式。
Front-door Reducibility: Reducing ADMGs to the Standard Front-door Setting via a Graphical Criterion
- 通过变量聚类形成超级节点，用图形条件判断是否可化为标准前门结构。
- 算法能准确找出可简化三元组，结果简单可估计，比通用识别公式更易用。
- 适合追求可解释性的因果推断研究者，尤其处理混合图时优势明显。
前门调整在经典前门准则下提供简洁的闭式识别公式，但适用范围常被认为狭窄。相比之下，通用识别（ID）算法可在任意图中识别更多因果效应，但通常输出代数复杂、难以估计和解释的表达式。本文提出前门可约性（FDR），一种针对无环有向混合图（ADMG）的图形条件，可通过将变量聚类为超节点（$\boldsymbol{X}^{*},\boldsymbol{Y}^{*},\boldsymbol{M}^{*}$）将许多复杂图转化为标准前门设置。我们刻画了FDR判据，证明其与存在有效FDR调整等价，并提出FDR-TID算法，该算法具备正确性、完备性和有限终止性保证。实证示例显示，许多远超教科书前门设定的图也满足FDR，从而获得简洁且可估计的调整方案，而通用ID表达式则会非常繁琐。因此，FDR在不牺牲混合图普适性的前提下，以可解释性和计算简便性补充现有识别方法。
原文摘要 · Abstract (English)
Front-door adjustment gives a simple closed-form identification formula under the classical front-door criterion, but its applicability is often viewed as narrow. By contrast, the general ID algorithm can identify many more causal effects in arbitrary graphs, yet typically outputs algebraically complex expressions that are hard to estimate and interpret. We show that many such graphs can in fact be reduced to a standard front-door setting via front-door reducibility (FDR), a graphical condition on acyclic directed mixed graphs that aggregates variables into super-nodes $(\boldsymbol{X}^{*},\boldsymbol{Y}^{*},\boldsymbol{M}^{*})$. We characterize the FDR criterion, prove it is equivalent (at the graph level) to the existence of an FDR adjustment, and present FDR-TID, an exact algorithm that finds an admissible FDR triple with correctness, completeness, and finite-termination guarantees. Empirical examples show that many graphs far outside the textbook front-door setting are FDR, yielding simple, estimable adjustments where general ID expressions would be cumbersome. FDR therefore complements existing identification methods by prioritizing interpretability and computational simplicity without sacrificing generality across mixed graphs.
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