This paper discusses algorithms for learning causal DAGs. The PC algorithm makes no assumptions other than the faithfulness to the causal model and can identify only up to the Markov equivalence class. LiNGAM assumes linearity and continuous non-Gaussian disturbances for the causal model, and the causal DAG defining LiNGAM is shown to be fully identifiable. The PC-LiNGAM, a hybrid of the PC algorithm and LiNGAM, can identify up to the distribution-equivalence pattern of a linear causal model, even in the presence of Gaussian disturbances. However, in the worst case, the PC-LiNGAM has factorial time complexity for the number of variables. In this paper, we propose an algorithm for learning the distribution-equivalence patterns of a linear causal model with a lower time complexity than PC-LiNGAM, using the causal ancestor finding algorithm in Maeda and Shimizu, which is generalized to account for Gaussian disturbances.

本研究解决了现有因果模型学习算法在Gaussian噪声下的效率问题。通过提出一种基于Maeda和Shimizu的祖先寻找算法的新方法，论文实现了比PC-LiNGAM更低的时间复杂度，进而有效识别线性因果模型的分布等价模式。该算法在推广时考虑了高斯干扰，为因果推断提供了更高效的工具。

利用祖先关系学习包含高斯噪声的线性无环因果模型