Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles
This addresses a fundamental limitation in causal discovery for complex systems with cycles, providing theoretical guarantees for existing algorithms in scenarios previously assumed to be acyclic.
The paper tackles the problem of causal discovery in systems with feedback loops, showing that the Fast Causal Inference (FCI) algorithm correctly estimates causal relations, direct causal relations, absence of confounders, and absence of specific cycles from observational data generated by a simple and σ-faithful Structural Causal Model.
While feedback loops are known to play important roles in many complex systems, their existence is ignored in a large part of the causal discovery literature, as systems are typically assumed to be acyclic from the outset. When applying causal discovery algorithms designed for the acyclic setting on data generated by a system that involves feedback, one would not expect to obtain correct results. In this work, we show that -- surprisingly -- the output of the Fast Causal Inference (FCI) algorithm is correct if it is applied to observational data generated by a system that involves feedback. More specifically, we prove that for observational data generated by a simple and $σ$-faithful Structural Causal Model (SCM), FCI is sound and complete, and can be used to consistently estimate (i) the presence and absence of causal relations, (ii) the presence and absence of direct causal relations, (iii) the absence of confounders, and (iv) the absence of specific cycles in the causal graph of the SCM. We extend these results to constraint-based causal discovery algorithms that exploit certain forms of background knowledge, including the causally sufficient setting (e.g., the PC algorithm) and the Joint Causal Inference setting (e.g., the FCI-JCI algorithm).