A constraint-based algorithm for causal discovery with cycles, latent variables and selection bias

Causal processes in nature may contain cycles, and real datasets may violate causal sufficiency as well as contain selection bias. No constraint-based causal discovery algorithm can currently handle cycles, latent variables and selection bias (CLS) simultaneously. I therefore introduce an algorithm called cyclic causal inference (CCI) that makes sound inferences with a conditional independence oracle under CLS, provided that we can represent the cyclic causal process as a non-recursive linear structural equation model with independent errors. Empirical results show that CCI outperforms the cyclic causal discovery algorithm in the cyclic case as well as rivals the fast causal inference and really fast causal inference algorithms in the acyclic case. An R implementation is available at https://github.com/ericstrobl/CCI.