Learning high-dimensional directed acyclic graphs with latent and selection variables

TL;DR

This paper introduces RFCI, a faster alternative to FCI for learning causal structures in high-dimensional DAGs with latent variables, ensuring asymptotic correctness despite reduced informational output.

Contribution

The paper proposes RFCI, a computationally efficient algorithm for causal discovery in high-dimensional DAGs with latent variables, with proven asymptotic correctness and comparable performance to FCI.

Findings

RFCI is significantly faster than FCI for large graphs.

RFCI's causal inferences are correct asymptotically.

Simulation studies show similar estimation performance between RFCI and FCI.

Abstract

We consider the problem of learning causal information between random variables in directed acyclic graphs (DAGs) when allowing arbitrarily many latent and selection variables. The FCI (Fast Causal Inference) algorithm has been explicitly designed to infer conditional independence and causal information in such settings. However, FCI is computationally infeasible for large graphs. We therefore propose the new RFCI algorithm, which is much faster than FCI. In some situations the output of RFCI is slightly less informative, in particular with respect to conditional independence information. However, we prove that any causal information in the output of RFCI is correct in the asymptotic limit. We also define a class of graphs on which the outputs of FCI and RFCI are identical. We prove consistency of FCI and RFCI in sparse high-dimensional settings, and demonstrate in simulations that the estimation performances of the algorithms are very similar. All software is implemented in the R-package pcalg.