Local Constraint-Based Causal Discovery under Selection Bias

We consider the problem of discovering causal effects from independence constraints when both selection bias and confounding are present. While the seminal FCI algorithm is sound and complete in this setup, no criterion for interpreting causal relations from its PAG output under selection bias is presently known. We instead focus on local constraint-based patterns between three or four variable patterns. The LCD algorithm is seen to fail in these conditions, while the four variable (Extended) Y-Structure is shown to be asymptotically sound in predicting causal effects when selection bias and latent confounding are present. We introduce a finite-sample scoring rule for Y-Structures that is shown to successfully predict ancestral causal effects in simulation experiments where selection bias is introduced. In a real-world setting, we show how Y-Structures perform well across different datasets, potentially circumventing spurious correlations due to selection bias.