Local Constraint-Based Causal Discovery in the Presence of Cycles and Latent Variables

Local causal discovery is of practical importance because many practical needs call only for identifying the causal structure surrounding a single target variable, making recovery of the entire global structure unnecessary. However, existing local methods typically assume acyclicity or the absence of latent variables. We study local causal discovery when cycles and latent variables are both present. We first characterize a local region sufficient for target-specific structure learning and establish which locally learned causal information is consistent with that obtained from global discovery. Building on these results, we propose a local constraint-based algorithm and prove that, under standard assumptions, it is sound and complete, recovering the same identifiable structure around the target as global causal discovery. Extensive experiments on random and real-world structures demonstrate the effectiveness and efficiency of our method.