Nonparametric Causal Structure Learning in High Dimensions

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.

Automated summary

The PC and FCI algorithms are popular methods for learning DAGs. However, these algorithms rely on the assumption of joint Gaussianity, which may not hold in many applications. In order to address this limitation, we propose nonparametric variants of the PC-stable and FCI-stable algorithms that use conditional distance covariance (CdCov) to test for conditional independence. Numerical studies show that our proposed algorithms perform well for both Gaussian and non-Gaussian graphical models.