Abstract: To address the problems of decreased accuracy in causal structure learning and unreliable causal direction determination among observed variables under latent-variable interference, a latent variable causal discovery method based on non-Gaussian information is proposed. In real-world data, there often exist latent variables that cannot be directly observed or completely recorded. These latent variables may simultaneously affect multiple observed variables, thereby inducing statistical correlations among observed variables due to common causes. Causal discovery methods that do not consider the existence of latent variables tend to misinterpret such latent-variable-induced correlations as causal relationships, resulting in spurious causal edges, incorrect causal directions, and incomplete structure recovery. To improve the accuracy of causal structure recovery in scenarios with latent variables, the proposed method utilizes the non-Gaussian information contained in data under a linear non-Gaussian acyclic causal model with latent variables, and identifies both direct causal relationships among observed variables and undirected causal relationships affected by latent variables. Specifically, in the first stage, the method takes a complete undirected graph over observed variables as the initial structure, and gradually removes statistically independent variable pairs through conditional independence tests based on regression residuals, thereby obtaining an initial skeleton structure among observed variables. This stage can preferentially determine some reliable direct causal relationships among observed variables without explicitly modeling latent variables, providing a structural basis for subsequent latent variable detection and orientation of remaining edges. In the second stage, for variable relationships that remain unoriented and may be affected by latent variables, higher-order cumulants are introduced to characterize the higher-order statistical information in non-Gaussian distributions. Fourth-order joint cumulants are used to estimate the effect strength of latent variables on observed variables, and whether multiple observed variables are affected by a common latent variable is determined by testing whether the shared single latent component condition is satisfied. On this basis, the remaining unoriented edges among observed variables affected by latent variables are further oriented, and a causal structure containing both observed variables and latent variables is finally output. Theoretical analysis shows that, when the variables are generated by a linear non-Gaussian acyclic causal model, the noise variables are mutually independent, and the relevant identifiability conditions hold, the proposed method can identify causal structures with latent variables by using independence constraints and higher-order cumulant information. To verify the effectiveness of the method, the proposed method is compared with several representative methods under five simulated causal graphs and three sample-size settings. Experimental results show that the proposed method maintains relatively high precision in most scenarios, with precision at least 30% higher than that of existing methods. Meanwhile, the proposed method achieves the best results in both recall and F1-score, and its F1-score is greater than or equal to 75% under different sample sizes. In particular, in simulated scenarios with strong latent-variable effects and complex structures, the proposed method can effectively reduce the omission of true causal edges and improve the overall structure recovery ability. Ablation experiments show that both the local structure identification stage without latent-variable interference and the stage of latent variable detection and unoriented causal edge identification play important roles in final causal structure recovery. In the real-world financial data experiment, return data of multiple constituent stocks in the Hong Kong stock market are used to further verify the applicability of the proposed method in practical scenarios. Experimental results show that the proposed method can identify latent variable structures with clear economic meanings while maintaining reasonable sparsity of the causal graph, and can characterize a multi-level causal transmission relationship from market-wide macro factors to industry sectors and then to individual stocks. Compared with several representative methods, the proposed method avoids the problem of overly dense causal graphs and compensates for the limitations of some methods that lack global driving factors or do not explicitly characterize latent variable structures. Overall, the results of simulation experiments, ablation experiments, and real-world data experiments demonstrate that the proposed method can effectively utilize higher-order statistical information and conditional independence constraints, improve the accuracy, completeness, and interpretability of causal structure recovery in scenarios with latent variables, and provide an effective approach for causal analysis and intelligent decision-making in complex data environments.

摘要： 针对存在隐变量干扰时因果结构学习准确性下降、观测变量间因果方向难以可靠判断的问题，提出一种基于非高斯信息的隐变量因果发现方法。实际数据中往往存在无法直接观测或难以完整记录的隐变量，这些隐变量会同时影响多个观测变量，使观测变量之间出现由共同原因导致的统计相关关系。不考虑隐变量存在的因果发现方法容易将隐变量诱导的相关性误判为因果关系，进而产生虚假因果边、因果方向错误和结构恢复不完整等问题。为提高含隐变量场景下因果结构恢复的准确性，所提方法在含隐变量的线性非高斯无环因果模型下，利用数据的非高斯信息，对观测变量间的直接因果关系以及隐变量影响下的未定向因果关系进行识别。具体而言，在第一阶段中，方法以观测变量构成的完全无向图作为初始结构，通过基于回归残差的条件独立性检验逐步删除统计独立的变量对，从而获得观测变量间的初始骨架结构。该阶段能够在不显式建模隐变量的情况下，优先确定部分可靠的观测变量间直接因果关系，为后续隐变量检测和剩余边定向提供结构基础。在第二阶段中，针对仍未完全定向且可能受到隐变量影响的变量关系，引入高阶累积量刻画非高斯分布中的高阶统计信息。通过采用四阶联合累积量估计隐变量对观测变量的作用强度，并通过检验是否满足共享单隐成分条件，判断多个观测变量是否受到共同隐变量影响。在此基础上，进一步对受隐变量影响的观测变量间剩余未定向边进行方向判定，最终输出包含观测变量及隐变量的因果结构。理论分析表明，在变量由线性非高斯无环因果模型生成、噪声变量相互独立且相关可识别条件成立的情况下，所提方法能够利用独立性约束和高阶累积量信息识别含隐变量因果结构。为验证方法有效性，在5种模拟因果图和3种样本量设置下，将所提方法与多种代表性方法进行比较。实验结果表明，所提方法在多数场景下精确率较高，比现有方法的精确率至少高30%。同时，所提方法在召回率和F1得分上均取得最优结果，在不同样本量下的F1评分大于或等于75%。特别是在隐变量影响较强、结构较复杂的模拟场景中，所提方法能够有效减少真实因果边遗漏，提高整体结构恢复能力。消融实验表明，所提方法中无隐变量干扰局部结构识别，以及隐变量检测与未定向因果边识别两个阶段均对最终因果结构恢复具有重要作用。在真实金融数据实验中，以香港股票市场中多只成分股收益数据为研究对象，进一步验证所提方法在实际场景中的适用性。实验结果显示，所提方法能够在保持因果图合理稀疏性的同时，识别出具有明确经济含义的隐变量结构，刻画从全市场宏观因子到行业板块再到个体股票的多层级因果传导关系。与多种代表性方法相比，所提方法既避免了因果图边过密的问题，也弥补了部分方法缺乏全局驱动因子或未显式刻画隐变量结构的不足。综合模拟实验、消融实验和真实数据实验结果可知，所提方法能够有效利用高阶统计信息和条件独立性约束，提高含隐变量场景下因果结构恢复的准确性、完整性与可解释性，为复杂数据环境下的因果分析和智能决策提供了一种有效方法。