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While feedback loops are known to play important roles in many complexsystems, their existence is ignored in a large part of the causal discoveryliterature, as systems are typically assumed to be acyclic from the outset.When applying causal discovery algorithms designed for the acyclic setting ondata generated by a system that involves feedback, one would not expect toobtain correct results. In this work, we show that -- surprisingly -- theoutput of the Fast Causal Inference (FCI) algorithm is correct if it is appliedto observational data generated by a system that involves feedback. Morespecifically, we prove that for observational data generated by a simple and$\sigma$-faithful Structural Causal Model (SCM), FCI is sound and complete, andcan be used to consistently estimate (i) the presence and absence of causalrelations, (ii) the presence and absence of direct causal relations, (iii) theabsence of confounders, and (iv) the absence of specific cycles in the causalgraph of the SCM. We extend these results to constraint-based causal discoveryalgorithms that exploit certain forms of background knowledge, including thecausally sufficient setting (e.g., the PC algorithm) and the Joint CausalInference setting (e.g., the FCI-JCI algorithm).

Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles