LiNGAM determines the variable order from cause to effect using additive noise models, but it faces challenges with confounding. Previous methods maintained LiNGAM's fundamental structure while trying to identify and address variables affected by confounding. As a result, these methods required significant computational resources regardless of the presence of confounding, and they did not ensure the detection of all confounding types. In contrast, this paper enhances LiNGAM by introducing LiNGAM-MMI, a method that quantifies the magnitude of confounding using KL divergence and arranges the variables to minimize its impact. This method efficiently achieves a globally optimal variable order through the shortest path problem formulation. LiNGAM-MMI processes data as efficiently as traditional LiNGAM in scenarios without confounding while effectively addressing confounding situations. Our experimental results suggest that LiNGAM-MMI more accurately determines the correct variable order, both in the presence and absence of confounding.

翻译：LiNGAM通过加性噪声模型确定从原因到结果的变量顺序，但在处理混杂问题时面临挑战。以往方法在保持LiNGAM基本结构的同时，试图识别并处理受混杂影响的变量。因此，无论是否存在混杂，这些方法都需要大量计算资源，且无法确保检测所有类型的混杂。相比之下，本文通过引入LiNGAM-MMI方法对LiNGAM进行改进：该方法利用KL散度量化混杂强度，并通过排列变量以最小化其影响。通过最短路径问题的形式化，该方法能高效获得全局最优的变量顺序。在无混杂场景下，LiNGAM-MMI的数据处理效率与传统LiNGAM相当，同时能有效处理混杂情况。实验结果表明，无论是否存在混杂，LiNGAM-MMI均能更准确地确定正确的变量顺序。