arXiv:2604.09309stat.MLcs.LG2026-04

提出迭代识别闭包,让因果模型能自动解锁更多未知效应。

Iterative Identification Closure: Amplifying Causal Identifiability in Linear SEMs

  • 先用外部信息找初始可识别边,再逐轮利用已知系数推导新边
  • 在5节点图上实现100%准确识别,比传统方法多解80%以上边
  • 适合处理有隐变量的复杂因果模型,尤其对小样本研究有帮助

半轨准则(HTC)是判断含潜变量线性结构方程模型中因果效应可识别性的主要图形工具。但其为节点级方法,同时处理一个节点的所有入边,导致中等规模图中15%-23%的因果效应无法判定。本文提出迭代识别闭包(IIC),将识别过程分为两阶段:(1) 初始种子函数 S_0,从工具变量、干预、非高斯性、先验知识等外部信息中识别一组初始边;(2) 降维的HTC传播,通过代入已知系数降低系统维度,从而识别标准HTC无法处理的边。核心创新在于迭代反馈机制:新识别的边可反向激活更多识别,这是现有图形准则所缺乏的。该机制需证明修正后雅可比矩阵仍保持通用满秩——为此提出新的理论结果(降维HTC定理)。证明IIC具有正确性、单调性,在最多|E|次迭代内收敛(实际常≤2次),并严格包含HTC与祖先分解。对n≤5的所有图(共134,144条边)的穷举验证显示100%精度(零误报);结合多个种子后,IIC使HTC缺口减少超80%。传播增益达γ~4×(2个种子识别约3%边,最终实现97.5%识别),远超此前无迭代反馈方法的γ≤1.2×。

原文摘要 · Abstract (English)

The Half-Trek Criterion (HTC) is the primary graphical tool for determining generic identifiability of causal effect coefficients in linear structural equation models (SEMs) with latent confounders. However, HTC is inherently node-wise: it simultaneously resolves all incoming edges of a node, leaving a gap of "inconclusive" causal effects (15-23% in moderate graphs). We introduce Iterative Identification Closure (IIC), a general framework that decouples causal identification into two phases: (1) a seed function S_0 that identifies an initial set of edges from any external source of information (instrumental variables, interventions, non-Gaussianity, prior knowledge, etc.); and (2) Reduced HTC propagation that iteratively substitutes known coefficients to reduce system dimension, enabling identification of edges that standard HTC cannot resolve. The core novelty is iterative identification propagation: newly identified edges feed back to unlock further identification -- a mechanism absent from all existing graphical criteria, which treat each edge (or node) in isolation. This propagation is non-trivial: coefficient substitution alters the covariance structure, and soundness requires proving that the modified Jacobian retains generic full rank -- a new theoretical result (Reduced HTC Theorem). We prove that IIC is sound, monotone, converges in O(|E|) iterations (empirically <=2), and strictly subsumes both HTC and ancestor decomposition. Exhaustive verification on all graphs with n<=5 (134,144 edges) confirms 100% precision (zero false positives); with combined seeds, IIC reduces the HTC gap by over 80%. The propagation gain is gamma~4x (2 seeds identifying ~3% of edges to 97.5% total identification), far exceeding gamma<=1.2x of prior methods that incorporate side information without iterative feedback.

因果推断结构方程可识别性

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