Nonparametric causal structure learning in high dimensions

TL;DR

This paper introduces nonparametric variants of causal structure learning algorithms that use conditional distance covariance, enabling consistent high-dimensional learning beyond Gaussian assumptions.

Contribution

It develops nonparametric versions of PC-stable and FCI-stable algorithms using CdCov, with proven high-dimensional consistency for general distributions.

Findings

Algorithms perform comparably to Gaussian-based methods on Gaussian data.

Proposed methods outperform in non-Gaussian models.

Theoretical guarantees extend to broader distribution classes.

Abstract

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.