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针对基于约束的因果关系发现方法中的马尔科夫等价类问题及函数因果模型对噪声的非高斯性假设问题，使用Cai-伪残差的三个定理，提出了Cai-伪残差因果定向算法。首先，假设变量之间关系线性且不限制噪声类型，在此条件下，对于贝叶斯网络的三种结构，Cai-伪残差与变量间的独立性表现出不同的结果。其次，利用基于约束的方法构建马尔科夫等价类之后，通过不同结果进一步发现并区分三种结构，对马尔科夫等价类中部分未定向的边进一步定向。最后，在不同因果网络构成的线性高斯数据集和线性非高斯数据集上分别进行了实验，结果表明，所提算法不仅显著减少了马尔科夫等价类中无向边的数量，同时也有效地提高了因果关系定向的准确性。
Abstract：In addressing the issues of Markov equivalence class in constraint-based causal discovery methods and the non-Gaussian noise assumption in functional causal models, the Cai-pseudo residual causal orientation algorithm was proposed using the three theorems of the Cai-pseudo residuals. Firstly, the relationships between variables were assumed to be linear, and no restrictions were imposed on the type of noise. With these conditions, the independence between the Cai-pseudo residuals and variables was manifested in diverse ways across the three distinct structures of Bayesian networks. Secondly, after construction of the Markov equivalence class using a constraint-based method, such varying associations were exploited to further distinguish the three structures and direct some previously undirected edges within the Markov equivalence class. Finally, experiments were performed on both linear Gaussian datasets and non-Gaussian datasets made up of different causal network structures. The results highlighted that the proposed algorithm not only greatly lessened the quantity of undirected edges in the Markov equivalence class, but also notably enhanced the accuracy of causal direction determination.
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基本信息:
DOI：10.13705/j.issn.1671-6841.2024102
中图分类号:TP18
引用信息:
[1]牛瑞琪,原泽鹏,翟岩慧等.基于Cai-伪残差与变量独立性的因果定向方法[J].郑州大学学报(理学版),2025,57(06):24-33.DOI:10.13705/j.issn.1671-6841.2024102.
基金信息:
国家自然科学基金项目(62072294,61972238)