On the Completeness of Causal Discovery in the Presence of Latent Confounding with Tiered Background Knowledge

The discovery of causal relationships is a core part of scientific research. Accordingly, over the past several decades, algorithms have been developed to discover the causal structure for a system of variables from observational data. Learning ancestral graphs is of particular interest due to their ability to represent latent confounding implicitly with bi-directed edges. The well-known FCI algorithm provably recovers an ancestral graph for a system of variables encoding the sound and complete set of causal relationships identifiable from observational data. Additional causal relationships become identifiable with the incorporation of background knowledge; however, it is not known for what types of knowledge FCI remains complete. In this paper, we define tiered background knowledge and show that FCI is sound and complete with the incorporation of this knowledge.