The PC and FCI algorithms are popular constraint-based methods for learning the structure of directed acyclic graphs (DAGs) in the absence and presence of latent and selection variables, respectively. These algorithms (and their order-independent variants, PC-stable and FCI-stable) have been shown to be consistent for learning sparse high-dimensional DAGs based on partial correlations. However, inferring conditional independences from partial correlations is valid if the data are jointly Gaussian or generated from a linear structural equation model -- an assumption that may be violated in many applications. To broaden the scope of high-dimensional causal structure learning, we propose nonparametric variants of the PC-stable and FCI-stable algorithms that employ the conditional distance covariance (CdCov) to test for conditional independence relationships. As the key theoretical contribution, we prove that the high-dimensional consistency of the PC-stable and FCI-stable algorithms carry over to general distributions over DAGs when we implement CdCov-based nonparametric tests for conditional independence. Numerical studies demonstrate that our proposed algorithms perform nearly as good as the PC-stable and FCI-stable for Gaussian distributions, and offer advantages in non-Gaussian graphical models.
翻译:PC 和 FCI 算法是在没有和存在潜在和选择变量的情况下分别学习定向单极图结构的流行约束性方法。这些算法(及其顺序独立的变异、PC-sable和FCI-sable)已证明在根据部分相关关系学习稀疏高维DAG方面是一致的。然而,如果数据是联合高沙或线性结构方程模型生成的数据,则从部分相关性推断有条件独立是有效的 -- -- 在许多应用中可能违反这一假设。为了扩大高维因果结构学习的范围,我们提出了采用有条件远程共变异(CdCov)的PC-Sable和FCI-sable等式非参数非参数变量,以测试有条件独立关系。作为关键理论贡献,我们证明,当我们实施基于CdCov的非参数的因果性因果性结构学测试时,PC-s-Squalalalal 算法的高度一致性将超过DAGs。Nomicalalals 研究显示,我们在有条件独立时,我们提出的C-Civilal-Agal-s 的分布式模型几乎是好的。