用可解释的符号树恢复因果机制，让黑箱模型变透明。
EML-CD: Causal Mechanism Recovery via EML Symbolic Trees in Structure Learning
- 用单个二元运算符构建符号树表示每个因果关系，自动推导闭式方程。
- 在真实数据上结构误差SHD=11.2，同时为每条边生成可读方程。
- 适合需要理解因果机制的科研与医疗领域，尤其看重可解释性。
基于神经网络的非线性因果发现方法虽能恢复有向无环图（DAG）结构，但各因果机制仍为黑箱。本文提出EML-CD框架，将具备组合基础函数能力的EML算子融入结构学习，以可解释机制恢复为核心目标。该方法将每条边的机制表示为带门控的EML二叉树，自动发现闭式因果方程。可直接从方程计算解析雅可比矩阵，实现因果效应的定量分析。在真实数据（Sachs蛋白信号，d=11）上，EML-CD达到均值SHD=11.2±0.4（5种子平均），性能与PC/GES相当且优于CAM，同时为每个检测到的边附带闭式方程（精确率0.756，召回率0.365）。在已知机制的双变量控制实验中，成功恢复11种基本函数中的10种（保留形状相关性≥0.96；仅高频正弦部分缺失）。在符号合成基准测试中，其机制预测均方误差（f-MSE）显著低于固定SINDy字典（均值3.67 vs. 7644），尽管结构恢复误差（SHD=14.0）仅与字典相当，不及专用优化器；在因果隧道光路子集上，深度2模型的F1得分优于线性OLS-BIC（0.444 vs. 0.273）。
原文摘要 · Abstract (English)
Neural network (NN)-based nonlinear causal discovery methods recover DAG structure but leave each causal mechanism as a black box. Waxman et al. argued that extracting causal mechanisms from NN weights is ill-posed. We propose EML-CD, a framework that integrates the EML operator (capable of composing elementary functions from a single binary operator) into causal structure learning, with interpretable mechanism recovery as the primary objective. EML-CD represents each edge mechanism as a gated EML binary tree and automatically discovers closed-form causal equations. Analytical Jacobians can be directly computed from the output equations, enabling quantitative understanding of causal effects. On real data (Sachs protein signaling, d=11), EML-CD achieves SHD=11.2 +/- 0.4 (5-seed mean; baselines are single deterministic runs), on par with PC/GES within seed variance and below CAM, while attaching closed-form equations to each detected edge (precision 0.756, recall 0.365). In a controlled bivariate test with known mechanisms, EML-CD recovers 10 of 11 elementary function families faithfully (held-out shape correlation >= 0.96; only high-frequency sine is partial). On a symbolic synthetic benchmark, EML-CD attains a substantially lower and more stable held-out mechanism f-MSE than a fixed SINDy dictionary (mean 3.67 vs. 7644, the latter inflated by catastrophic extrapolation on one seed), although its structure recovery (SHD 14.0) only matches the dictionary and stays below specialized optimizers; on the Causal Chambers light-tunnel subset, a depth-2 model improves F1 over linear OLS-BIC (0.444 vs. 0.273).
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