A Causal Structure Learning Algorithm with Dynamic Weighted Condition Set

CAO Dong-lei; CAO Fu-yuan; WANG Yun-xia; GAO Xiao-fang

doi:10.12263/DZXB.20250637

您当前的位置：

首页 >

文章列表页 >

A Causal Structure Learning Algorithm with Dynamic Weighted Condition Set

PAPERS | 更新时间：2025-12-27

- A Causal Structure Learning Algorithm with Dynamic Weighted Condition Set
- ACTA ELECTRONICA SINICA Vol. 53, Issue 9, Pages: 3274-3286(2025)
- 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：
- 基金信息：
  
  National Natural Science Foundation of China(U24A20323;62376145);Shanxi Province Science and Technology Innovation Talent Team Special Project(202204051002016);Key Technologies Program of Taihang Laboratory in Shanxi Province(THYF-JSZX-24010700)
- DOI：10.12263/DZXB.20250637
  CLC： TP18;
- Received：21 July 2025，
  
  Accepted：16 September 2025，
  
  Published：25 September 2025
- 稿件说明：
移动端阅览
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

SPIRTES P , ZHANG K . Causal discovery and inference: Concepts and recent methodological advances [J ] . Applied Informatics , 2016 , 3 : 3 .

PEARL J , MACKENZIE D . The book of why: The new science of cause and effect [J ] . Journal of the American Statistical Association , 2020 , 115 ( 529 ): 482 - 485 .

CAO F Y , WANG Y X , YU K , et al . Causal discovery from unknown interventional datasets over overlapping variable sets [J ] . IEEE Transactions on Knowledge and Data Engineering , 2024 , 36 ( 12 ): 7725 - 7742 .

NEUBERG L G . Causality: Models, reasoning, and inference [J ] . Econometric Theory , 2003 , 19 ( 4 ): 675 - 685 .

CAI R C , ZHANG Z J , HAO Z F , et al . Understanding social causalities behind human action sequences [J ] . IEEE Transactions on Neural Networks and Learning Systems , 2017 , 28 ( 8 ): 1801 - 1813 .

RUNGE J , NOWACK P , KRETSCHMER M , et al . Detecting and quantifying causal associations in large nonlinear time series datasets [J ] . Science Advances , 2019 , 5 ( 11 ): eaau4996 .

CAI R C , ZHANG Z J , HAO Z F . Causal gene identification using combinatorial V-structure search [J ] . Neural Networks , 2013 , 43 : 63 - 71 .

YANG J , AN N , ALTEROVITZ G . A partial correlation statistic structure learning algorithm under linear structural equation models [J ] . IEEE Transactions on Knowledge and Data Engineering , 2016 , 28 ( 10 ): 2552 - 2565 .

SHEN X P , MA S S , VEMURI P , et al . Challenges and opportunities with causal discovery algorithms: Application to Alzheime’s pathophysiology [J ] . Scientific Reports , 2020 , 10 : 2975 .

CHEN W Q , HAO Z F , CAI R C , et al . Multiple-cause discovery combined with structure learning for high-dimensional discrete data and application to stock prediction [J ] . Soft Computing , 2016 , 20 ( 11 ): 4575 - 4588 .

LI Y Z , TORRALBA A , ANANDKUMAR A , et al . Causal discovery in physical systems from videos [EB/OL ] . ( 2020-11-29 )[ 2025-07-21 ] . https://arxiv.org/abs/2007.00631 https://arxiv.org/abs/2007.00631 .

YANG J , LI N , AN N , et al . An efficient causal structure learning algorithm for linear arbitrarily distributed continuous data [J ] . The Journal of Supercomputing , 2020 , 76 ( 5 ): 3355 - 3363 .

BELTHANGADY C , GIAMPANIS S , JANKOVIC I , et al . Causal deep learning reveals the comparative effectiveness of antihyperglycemic treatments in poorly controlled diabetes [J ] . Nature Communications , 2022 , 13 : 6921 .

SCHÖLKOPF B , LOCATELLO F , BAUER S , et al . Toward causal representation learning [J ] . Proceedings of the IEEE , 2021 , 109 ( 5 ): 612 - 634 .

WANG Y , CAO F Y , YU K , et al . Federated causal structure learning with non-identical variable sets [C ] // Proceedings of the 42nd International Conference on Machine Learning . Cambridge : PMLR , 2025 : 302 - 324 .

HUEGLE J , HAGEDORN C , SCHLOSSER R . A KNN-based non-parametric conditional independence test for mixed data and application in causal discovery [C ] // Machine Learning and Knowledge Discovery in Databases: Research Track . Cham : Springer , 2023 : 541 - 558 .

ZHANG K , PETERS J , JANZING D , et al . Kernel-based conditional independence test and application in causal discovery [C ] // Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence . New York : ACM , 2011 : 804 - 813 .

YANG S J , CAO F Y , YU K , et al . Learning causal chain graph structure via alternate learning and double pruning [J ] . IEEE Transactions on Big Data , 2024 , 10 ( 4 ): 442 - 456 .

SPIRTES P , GLYMOUR C N , SCHEINES R , et al . Causation, Prediction, and Search [M ] . 2nd Ed . Cambridge, Mass : MIT Press , 2000 .

MURPHY K , SCHÖLKOPF B , COLOMBO D , et al . Order-independent constraint-based causal structure learning [J ] . Journal of Machine Learning Research , 2014 , 15 ( 1 ): 3741 - 3782 .

RAMSEY J , SPIRTES P , ZHANG J J . Adjacency-faithfulness and conservative causal inference [C ] // Proceedings of the 22th Conference on Uncertainty in Artificial Intelligence . New York : ACM , 2006 : 401 - 408 .

蔡瑞初 , 陈薇 , 张坤 , 等 . 基于非时序观察数据的因果关系发现综述 [J ] . 计算机学报 , 2017 , 40 ( 6 ): 1470 - 1490 .

CAI R C , CHEN W , ZHANG K , et al . A survey on non-temporal series observational data based causal discovery [J ] . Chinese Journal of Computers , 2017 , 40 ( 6 ): 1470 - 1490 . (in Chinese)

郝志峰 , 汪菲霞 , 陈正鸣 , 等 . 基于增强条件独立性检验的鲁棒因果发现算法 [J ] . 软件学报 , 2025 , 36 ( 9 ): 4134 - 4152 .

HAO Z F , WANG F X , CHEN Z M , et al . Robust causal discovery algorithm based on enhanced conditional independence tests [J ] . Journal of Software , 2025 , 36 ( 9 ): 4134 - 4152 . (in Chinese)

MARGARITIS D , THRUN S . Bayesian network induction via local neighborhoods [C ] // Proceedings of the 13th International Conference on Neural Information Processing Systems . New York : ACM , 1999 : 505 - 511 .

ZHALAMA Z , ZHANG J J , EBERHARDT F , et al . ASP-based discovery of semi-Markovian causal models under weaker assumptions [C ] // Proceedings of the 28th International Joint Conference on Artificial Intelligence . California : IJCA , 2019 : 1488 - 1494 .

RUSSO F , TONI F . Shapley-PC: Constraint-based causal structure learning with Shapley values [C ] // Proceedings of the 4th Conference on Causal Learning and Reasoning . Lausanne, Switzerland : PMLR , 2025 : 292 - 339 .

AUMANN R J , HART S . Handbook of Game Theory with Economic Applications [M ] . Amsterdam,Tokyo : Elsevier , 1992 .

SUNDARARAJAN M , NAJMI A . The many Shapley values for model explanation [C ] // Proceedings of the 37th International Conference on Machine Learning . New York : ACM , 2020 : 9269 - 9278 .

ROZEMBERCZKI B , WATSON L , BAYER P , et al . The shapley value in machine learning [C ] // Proceedings of the 31th International Joint Conference on Artificial Intelligence . Vienna : IJCAI , 2022 : 5572 - 5579 .

曹付元 , 杨淑晶 , 王雲霞 , 等 . 基于约束的局部-全局LWF链图结构学习算法 [J ] . 电子学报 , 2023 , 51 ( 6 ): 1458 - 1467 .

CAO F Y , YANG S J , WANG Y X , et al . Local-global LWF chain graph structure learning algorithm based on constraints [J ] . Acta Electronica Sinica , 2023 , 51 ( 6 ): 1458 - 1467 . (in Chinese)

VOWELS M J , CAMGOZ N C , BOWDEN R . D’ya like DAGs? A survey on structure learning and causal discovery [J ] . ACM Computing Surveys , 2023 , 55 ( 4 ): 1 - 36 .

ZANGA A , OZKIRIMLI E , STELLA F . A survey on causal discovery: Theory and practice [J ] . International Journal of Approximate Reasoning , 2022 , 151 : 101 - 129 .

GLYMOUR C , ZHANG K , SPIRTES P . Review of causal discovery methods based on graphical models [J ] . Frontiers in Genetics , 2019 , 10 : 524 .

ALIFERIS C F , STATNIKOV A , TSAMARDINOS I , et al . Local causal and Markov blanket induction for causal discovery and feature selection for classification part I: Algorithms and empirical evaluation [J ] . Journal of Machine Learning Research , 2010 , 11 : 171 - 234 .

PETERS J , JANZING D , SCHÖLKOPF B . Elements of Causal Inference: Foundations and Learning Algorithms [M ] . Cambridge : MIT Press , 2017 .

PEARL J . The foundations of causal inference [J ] . Sociological Methodology , 2010 , 40 ( 1 ): 75 - 149 .

GONG C , ZHANG C Z , YAO D , et al . Causal discovery from temporal data: An overview and new perspectives [J ] . ACM Computing Surveys , 2024 , 57 ( 4 ): 1 - 38 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

No data

Related Author

CAO Fu-yuan

WANG Yun-xia

GAO Xiao-fang

Related Institution

No data

⁰