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.

研究了有向无环图中随意多个潜在变量和选择变量条件下因果信息的学习问题，在此设置中，提出了一种能够在计算上比 FCI 算法快得多的新算法 RFCI，虽然 RFCI 的输出在某些情况下比 FCI 输出略微不太具有信息性，但在渐近极限下 RFCI 的任何因果信息都是正确的，研究了一类图形，输出 FCI 和 RFCI 是相同的，并证明了 FCI 和 RFCI 在稀疏高维情况下的一致性。