Causal Discovery from Diverse Data

Causal discovery is increasingly applied across heterogeneous environments whose data-generating processes may differ substantially. Unlike standard multi-domain formulations based on hard or soft interventions, we do not assume that the domains arise from interventions on a common baseline graph: their causal graphs may differ structurally, including through edge additions, deletions, or reversals. We ask a fundamental question: how much causal knowledge can be learned by jointly exploiting such heterogeneous datasets? We show that mechanisms that remain stable across domains can induce cross-domain distributional invariances, even when other mechanisms and the underlying causal graphs differ. By systematically leveraging these invariances together with within-domain conditional independences, we identify the distributional constraints that such invariances impose on tuples of domain-specific causal graphs and characterize the resulting inv-Markov equivalence class. In particular, cross-domain invariances can reveal causal orientations that are not identifiable from any domain in isolation. Our algorithm can leverage cross-domain invariances to learn cause-effect relations beyond what is learnable in each domain, even when the underlying causal graphs are arbitrarily different, such as having reversed edges. Building on this characterization, we develop Diverse-FCI, a constraint-based algorithm that learns domain-specific partially oriented graphs while exploiting pairwise cross-domain invariances. Under a faithfulness condition ensuring that the relevant cross-domain dependencies remain detectable after latent projection, we prove its soundness. Synthetic experiments show improved orientation recovery over learning each domain independently, with larger gains as structural heterogeneity increases.