Chakraborty Shubhadeep, Shojaie Ali
Department of Biostatistics, University of Washington, Seattle, WA 98195, USA.
Entropy (Basel). 2022 Feb 28;24(3):351. doi: 10.3390/e24030351.
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.
PC算法和FCI算法是分别在不存在和存在潜在变量及选择变量的情况下用于学习有向无环图（DAG）结构的流行的基于约束的方法。这些算法（及其与顺序无关的变体，即PC稳定算法和FCI稳定算法）已被证明在基于偏相关学习稀疏高维DAG方面是一致的。然而，如果数据是联合高斯分布的或由线性结构方程模型生成的，从偏相关推断条件独立性才是有效的，而这一假设在许多应用中可能会被违反。为了拓宽高维因果结构学习的范围，我们提出了PC稳定算法和FCI稳定算法的非参数变体，它们使用条件距离协方差（CdCov）来检验条件独立关系。作为关键的理论贡献，我们证明，当我们对条件独立性实施基于CdCov的非参数检验时，PC稳定算法和FCI稳定算法的高维一致性可以推广到DAG上的一般分布。数值研究表明，我们提出的算法对于高斯分布的性能几乎与PC稳定算法和FCI稳定算法一样好，并且在非高斯图形模型中具有优势。
