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

About

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.

Diego Colombo, Marloes H. Maathuis, Markus Kalisch, Thomas S. Richardson · 2011

Related benchmarks

Task	Dataset	Result
Bayesian network structure discovery	Hailfinder	SHD58	39
Causal Structure Learning	Sachs	SHD14	38
Causal Discovery	Child	F1 Score—	35
Causal Discovery	Alarm	SHD24	14
Causal Discovery	Insurance	F1 Score76	13
Causal Discovery	Mildew	F1 Score84	10
Causal Discovery	Win95pts	SHD102	10
Causal Discovery	Pigs	SHD276	10
Causal Structure Learning	Hailfinder	F1 Score88	8
Causal Structure Learning	Alarm	F1-score89	6