Adèle H. Ribeiro

Clément Yvernes, Emilie Devijver, Adèle H. Ribeiro et al.

Cluster DAGs (C-DAGs) provide an abstraction of causal graphs in which nodes represent clusters of variables, and edges encode both cluster-level causal relationships and dependencies arisen from unobserved confounding. C-DAGs define an equivalence class of acyclic causal graphs that agree on cluster-level relationships, enabling causal reasoning at a higher level of abstraction. However, when the chosen clustering induces cycles in the resulting C-DAG, the partition is deemed inadmissible under conventional C-DAG semantics. In this work, we extend the C-DAG framework to support arbitrary variable clusterings by relaxing the partition admissibility constraint, thereby allowing cyclic C-DAG representations. We extend the notions of d-separation and causal calculus to this setting, significantly broadening the scope of causal reasoning across clusters and enabling the application of C-DAGs in previously intractable scenarios. Our calculus is both sound and atomically complete with respect to the do-calculus: all valid interventional queries at the cluster level can be derived using our rules, each corresponding to a primitive do-calculus step.

Adèle H. Ribeiro, Dominik Heider

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 nonparametric 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.

Tara V. Anand, Adèle H. Ribeiro, Jin Tian et al.

Reasoning about the effect of interventions and counterfactuals is a fundamental task found throughout the data sciences. A collection of principles, algorithms, and tools has been developed for performing such tasks in the last decades (Pearl, 2000). One of the pervasive requirements found throughout this literature is the articulation of assumptions, which commonly appear in the form of causal diagrams. Despite the power of this approach, there are significant settings where the knowledge necessary to specify a causal diagram over all variables is not available, particularly in complex, high-dimensional domains. In this paper, we introduce a new graphical modeling tool called cluster DAGs (for short, C-DAGs) that allows for the partial specification of relationships among variables based on limited prior knowledge, alleviating the stringent requirement of specifying a full causal diagram. A C-DAG specifies relationships between clusters of variables, while the relationships between the variables within a cluster are left unspecified, and can be seen as a graphical representation of an equivalence class of causal diagrams that share the relationships among the clusters. We develop the foundations and machinery for valid inferences over C-DAGs about the clusters of variables at each layer of Pearl's Causal Hierarchy (Pearl and Mackenzie 2018; Bareinboim et al. 2020) - L1 (probabilistic), L2 (interventional), and L3 (counterfactual). In particular, we prove the soundness and completeness of d-separation for probabilistic inference in C-DAGs. Further, we demonstrate the validity of Pearl's do-calculus rules over C-DAGs and show that the standard ID identification algorithm is sound and complete to systematically compute causal effects from observational data given a C-DAG. Finally, we show that C-DAGs are valid for performing counterfactual inferences about clusters of variables.