一种条件集动态加权的因果结构学习算法

曹冬蕾; 曹付元; 王雲霞; 高小方

doi:10.12263/DZXB.20250637

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一种条件集动态加权的因果结构学习算法

学术论文 | 更新时间：2025-12-27

- 一种条件集动态加权的因果结构学习算法
- A Causal Structure Learning Algorithm with Dynamic Weighted Condition Set
- 电子学报 2025年53卷第9期页码：3274-3286
- 作者机构：
  
  1.山西大学计算机与信息技术学院，山西太原 030006
  2.山西大学计算智能与中文信息处理教育部重点实验室，山西太原 030006
- 作者简介：
  
  [ "曹冬蕾女，2001年1月出生于山西省大同市.山西大学计算机与信息技术学院硕士研究生.主要研究方向为机器学习与因果推断. E-mail: caodonglei@sxu.edu.cn" ]
  [ "曹付元男，1974年5月出生于山西省大同市.山西大学计算机与信息技术学院教授、博士生导师.主要研究方向为机器学习与因果推断. cfy@sxu.edu.cn" ]
  [ "王雲霞女，1996年6月出生于山西省朔州市.山西大学计算机与信息技术学院讲师.主要研究方向为机器学习与因果推断.wyx@sxu.edu.cn" ]
  [ "高小方女，1978年2月出生于山西省安泽县.山西大学计算机与信息技术学院副教授、硕士生导师.主要研究方向为数据挖掘与机器学习.gxfhtp@sxu.edu.cn" ]
- 基金信息：
  
  国家自然科学基金(U24A20323;62376145);山西省科技创新人才团队专项资助项目(202204051002016);太行山西省实验室技术攻关专项资助项目(THYF-JSZX-24010700)
- DOI：10.12263/DZXB.20250637
  中图分类号： TP18;
- 收稿：2025-07-21，
  
  录用：2025-09-16，
  
  纸质出版：2025-09-25
- 稿件说明：
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曹冬蕾, 曹付元, 王雲霞, 等. 一种条件集动态加权的因果结构学习算法[J]. 电子学报, 2025, 53(09): 3274-3286.

CAO Dong-lei, CAO Fu-yuan, WANG Yun-xia, et al. A Causal Structure Learning Algorithm with Dynamic Weighted Condition Set[J]. Acta Electronica Sinica, 2025, 53(09): 3274-3286.
曹冬蕾, 曹付元, 王雲霞, 等. 一种条件集动态加权的因果结构学习算法[J]. 电子学报, 2025, 53(09): 3274-3286. DOI：10.12263/DZXB.20250637

CAO Dong-lei, CAO Fu-yuan, WANG Yun-xia, et al. A Causal Structure Learning Algorithm with Dynamic Weighted Condition Set[J]. Acta Electronica Sinica, 2025, 53(09): 3274-3286. DOI：10.12263/DZXB.20250637

摘要

基于约束的因果结构学习算法具有不依赖特定函数模型假设的优势且计算效率较高，但其对撞结构定向阶段高度依赖特定条件集的条件独立性检验（Conditional Independence Test，CIT）结果. 尽管近来有研究者提出Shapley-PC算法利用Shapley值整合多个条件集检验以降低CIT误差的影响，但仍未充分考虑不同条件集对定向决策的具体影响，忽略部分关键条件集的重要性，降低定向准确性. 为此，本文提出一种条件集动态加权的因果结构学习算法（Dynamically Weighted Causal Structure Learning，DW-CSL）. 该方法核心机制为针对相同规模的条件集通过归一化

-value与Shapley值构建动态权重，细粒度地量化不同条件集对定向决策的贡献差异，从而显著抑制CIT误差在对撞结构中的定向传播. 具体而言，该方法首先基于PC-Stable框架构建因果骨架；其次在对撞结构定向阶段，基于Shapley值提出条件集动态加权的定向决策规则，通过归一化

-value量化条件集贡献差异，使不同条件集的CIT结果具有可比性，再将归一化值作为Shapley边际贡献的权重，实现对未遮蔽三元组的精准定向；最后通过Meek规则定向剩余无向边. 实验结果表明，在合成与基准数据上，该方法较对比方法在对撞结构识别准确性上平均提高4.75%，在边定向准确性上平均提高5.5%，有效提高了因果结构学习的稳定性和准确性.

Abstract

Constraint-based causal structure learning algorithms have the advantage of not relying on specific functional model assumptions and generally offer high computational efficiency. However

their V-structure orientation stage heavily depends on the results of conditional independence tests (CIT) on specific conditioning sets. Although the recently proposed Shapley-PC algorithm integrates multiple condition sets through Shapley value evaluation to mitigate CIT errors

it still fails to adequately account for the varying influence of different condition sets on orientation decisions

thereby overlooking the importance of certain key sets and reducing orientation accuracy. To address this issue

we propose a dynamically weighted causal structure learning (DW-CSL) algorithm. The core idea of the method is to combine normalized

-values with Shapley values to assign dynamic weights to condition sets of the same size

thereby finely quantifying their contribution differences to orientation decisions and effectively suppressing the propagation of CIT errors in V-structure orientatio

n. Specifically

the algorithm first constructs the causal skeleton based on the PC-Stable framework; then

during V-structure orientation

it introduces a dynamic weighted orientation rule that incorporates normalized

-values into Shapley value calculations

making CIT results from different condition sets comparable and enabling precise orientation of unshielded triples; finally

the remaining undirected edges are oriented using Meek’s rules. Experimental results on both synthetic and benchmark datasets demonstrate that

compared with baseline methods

DW-CSL improves V-structure recognition accuracy by an average of 4.75% and edge orientation accuracy by an average of 5.5%

thereby enhancing the stability and overall accuracy of causal structure learning.

关键词

Keywords

references

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