# Nonparametric causal structure learning in high dimensions

arXiv: https://arxiv.org/abs/2106.11415 · HTML: https://mlsanity.com/paper/2106.11415/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2021.

## Built on by (most cited first, 2 of 2)

- [The Dual PC Algorithm and the Role of Gaussianity for Structure Learning of Bayesian Networks](https://mlsanity.com/paper/2112.09036/) (2021)
- [Learning Directed Acyclic Graphs from Partial Orderings](https://mlsanity.com/paper/2403.16031/) (2024)

## Abstract (arXiv)

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.