Journal
ANNALS OF STATISTICS
Volume 40, Issue 1, Pages 294-321Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/11-AOS940
Keywords
Causal structure learning; FCI algorithm; RFCI algorithm; maximal ancestral graphs (MAGs); partial ancestral graphs (PAGs); high-dimensionality; sparsity; consistency
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Funding
- Swiss NSF [200021-129972]
- U.S. NSF [CRI 0855230]
- U.S. NIH [R01 AI032475]
- Direct For Computer & Info Scie & Enginr
- Division Of Computer and Network Systems [0855230] Funding Source: National Science Foundation
- Swiss National Science Foundation (SNF) [200021_129972] Funding Source: Swiss National Science Foundation (SNF)
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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.
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