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

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

2011-04-29

arxiv.org/abs/1104.5617v2

Statistics

Methodology

Scientific paper

We consider the problem of learning causal information between random variables in directed acyclic graph (DAGs) when allowing arbitrarily many latent and selection variables. The FCI algorithm (Spirtes et al., 1999) 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 a new algorithm, the 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. 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 \texttt{pcalg}.

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