Causal Discovery.pdf

The Fast Causal Inference (FCI) algorithm is sound and complete when applied to observational data generated by a cyclic causal system that satisfies the σ-separation Markov property and is σ-faithful. The algorithm can consistently estimate the presence and absence of causal relations, direct causal relations, absence of confounders, and absence of specific cycles in the causal graph. The results apply to any constraint-based causal discovery algorithm that solves the same task as FCI, including those that exploit background knowledge, such as the PC algorithm and the FCI-JCI algorithm. The FCI algorithm can handle hundreds or thousands of variables as long as the underlying causal model is sparse enough and is applicable in the presence of latent confounders. The σ-separation Markov property is a mild assumption that applies to a wide class of cyclic structural causal models with non-linear functional relationships between non-discrete variables. The σ-faithfulness assumption is a natural extension of the common faithfulness assumption used in the acyclic setting. The algorithm provides a practical causal discovery method for cyclic causal systems, improving upon the previous state-of-the-art in causal discovery for the σ-separation setting.