Learning high-dimensional DAGs with latent and selection variables (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 Fast Causal Inference algorithm (FCI) (Spirtes et al., 1999) has been explicitly designed to infer conditional independence and causal information in such settings. Despite its name, FCI is computationally very intensive for large graphs. Spirtes (2001) introduced a modified version of FCI, called Anytime FCI, which only performs conditional independence tests up to a pre-specified cutoff k. Anytime FCI is typically faster but less informative than FCI, but the causal interpretation of tails and arrowheads in its output is still sound. We propose an adaptation of Anytime FCI, called Adaptive Anytime FCI (AAFCI), where the cut-off k is set to the maximum size of the conditioning sets used to find the initial skeleton in FCI. Moreover, we propose a new algorithm, called Really Fast Causal Inference (RFCI), which has similar properties as AAFCI but is much faster for large sparse graphs. The complete paper is available at http://arxiv.org/abs/1104.5617.