dcFCI: Robust Causal Discovery Under Latent Confounding, Unfaithfulness, and Mixed Data.

Causal discovery is central to inferring causal relationships from observational data. In the presence of latent confounding, algorithms such as Fast Causal Inference (FCI) learn a Partial Ancestral Graph (PAG) representing the true model's Markov Equivalence Class. However, their correctness critically depends on empirical faithfulness, the assumption that observed (in)dependencies perfectly reflect those of the underlying causal model, which often fails in practice due to limited sample sizes. To address this, we introduce the first non-parametric score to assess a PAG's compatibility with observed data, even with mixed variable types. This score is both necessary and sufficient to characterize structural uncertainty and distinguish between distinct PAGs. We then propose data-compatible FCI (dcFCI), the first hybrid causal discovery algorithm to jointly address latent confounding, empirical unfaithfulness, and mixed data types. dcFCI integrates our score into an (Anytime)FCI-guided search that systematically explores, ranks, and validates candidate PAGs. Experiments on synthetic and real-world scenarios demonstrate that dcFCI significantly outperforms state-of-the-art methods, often recovering the true PAG even in small and heterogeneous datasets. Examining top-ranked PAGs further provides valuable insights into structural uncertainty, supporting more robust and informed causal reasoning and decision-making.