From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variables

arXiv 2604.22416 ↗First posted 24 Apr 2026cs.LG cs.AIcited by 0

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Abstract (arXiv)

Latent variables pose a fundamental obstacle to both causal discovery and inference. Local approaches exploiting direct neighborhood relations provide little beyond immediate dependencies. Cluster-level methods, though capable of broader reasoning, generally require cluster assignments or causal sufficiency in advance, conditions that are rarely satisfied in practice. Applying single-variable discovery at cluster resolution violates these conditions and thereby produces systematic bias. L2C (Local to Cluster Causal Abstraction) learns cluster structure from local causal patterns without manual variable-to-cluster mapping. The framework rests on a cluster reduction theorem: each cluster can be represented by at most three micro-variables, with no loss of macro-level identifiability. In the presence of latent variables, local discovery on maximal ancestral graphs recovers direct causes, effects, and V-structures, followed by cluster-level inference through a corresponding calculus on the resulting graph. Macro causal effects are formulated as joint interventions on the micro-variables within each target cluster. The framework is sound, atomically complete, and polynomially bounded. L2C establishes a direct connection from local micro-level information to macro causal reasoning in settings where clusters are unknown and latent variables are unavoidable.

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References · 20

2013Causal Inference in the Presence of Latent Variables and Selection Biascited by 166
2013Learning Sparse Causal Models is not NP-hardcited by 49
2019Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variablescited by 39
2022Causal Effect Identification in Cluster DAGscited by 36
2023Foundations of Causal Discovery on Groups of Variablescited by 22
2022Local Constraint-Based Causal Discovery under Selection Biascited by 16
2023Causal Discovery with Latent Confounders Based on Higher-Order Cumulantscited by 16
2021Integer Programming for Causal Structure Learning in the Presence of Latent Variablescited by 15
2022Vector causal inference between two groups of variablescited by 11
2024Local Causal Structure Learning in the Presence of Latent Variablescited by 11
2020Local search for efficient causal effect estimationcited by 9
2023Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairscited by 9

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2023Discovery and inference of a causal network with hidden confoundingcited by 8
2021Towards Efficient Local Causal Structure Learningcited by 7
2024Local Causal Discovery for Structural Evidence of Direct Discriminationcited by 6
2025Nonlinear Causal Discovery for Grouped Datacited by 5
2025Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clusteringcited by 5
2025Identifying Macro Causal Effects in a C-DMG over ADMGscited by 4
2024Local Learning for Covariate Selection in Nonparametric Causal Effect Estimation with Latent Variablescited by 3
2025Identifying Macro Causal Effects in C-DMGs over DMGscited by 3

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