为分层因果模型设计可扩展的分析管道,解决班级规模对学生成绩影响的精准评估问题。
Scalable and Versatile Identification for Hierarchical Structural Causal Models: A New Look at Project STAR

- 通过图变换与符号推导,自动识别分层因果效应
- 在STAR数据上验证,忽略层级结构会导致干预效果误判
- 提出可并行计算的表达式分解机制,支持大规模实际应用
STAR(学生-教师成就比)实验(1985年,美国田纳西州)是一个具有里程碑意义的分层数据集,旨在评估班级规模对学生表现的影响,观测值嵌套于班级之中。为在分层设置中编码班级层面的干预,我们开发了一个完整、可扩展、开源的分层结构因果模型(HSCM)分析流水线,连接符号识别与实际估计。该方法结合图变换、pyAgrum的do-演算实现因果效应的自动识别,将符号表达式转化为闭式HSCM公式,并基于拟合的局部概率模型进行数值估计。核心创新在于改进的抽象语法树(AST),将pyAgrum识别出的公式分解为独立的密度、期望和边缘化任务,支持并行与可扩展计算。我们在具有已知真值的标准HSCM模式和基准场景中验证了该流水线,随后应用于STAR幼儿园数学成绩数据。结果表明,忽略层级结构的扁平基线模型虽能恢复相关性,但无法正确编码班级干预;仅靠符号识别不足以实现实际的分层因果推断;可扩展估计与数值稳定性检验是科学推理的核心环节。
原文摘要 · Abstract (English)
The STAR (Student-Teacher Achievement Ratio) experiment (1985, Tennessee, USA) is a landmark hierarchical dataset designed to assess the impact of class size on student outcomes, with observations nested within classes. To encode class-level interventions in such hierarchical settings, we develop a complete, scalable, open-source pipeline for Hierarchical Structural Causal Models (HSCM) that bridges symbolic identification and practical estimation. Our approach integrates graph transformations, pyAgrum's do-calculus for automatic identification of causal effects, adaptation of symbolic expression into closed-form HSCM formulas, and numerical estimation from fitted local probability models. A key innovation is our adapted Abstract Syntax Tree (AST), which decomposes pyAgrum's identified formulas into independent density, expectation, and marginalization tasks, enabling parallel and scalable computation. We validate the pipeline on canonical HSCM motifs and benchmark scenarios with known ground truth, then apply it to STAR kindergarten mathematics outcomes. The results show that flat baselines (ignoring hierarchy) recover associations but fail to encode class-level interventions, and that symbolic identification alone is not enough for practical Hierarchical Structural Causal inference; scalable estimation and numerical stability checks are central parts of the scientific object.
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