Causal Discovery in Linear Models with Unobserved Variables and Measurement Error

[2407.19426] Causal Discovery in Linear Models with Unobserved Variables and Measurement Error Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2407.19426 (cs) [Submitted on 28 Jul 2024 ( v1 ), last revised 9 Apr 2026 (this version, v2)] Title: Causal Discovery in Linear Models with Unobserved Variables and Measurement Error Authors: Yuqin Yang , Mohamed Nafea , Negar Kiyavash , Kun Zhang , AmirEmad Ghassami View a PDF of the paper titled Causal Discovery in Linear Models with Unobserved Variables and Measurement Error, by Yuqin Yang and 4 other authors View PDF HTML (experimental) Abstract: The presence of unobserved common causes and measurement error poses two major obstacles to causal structure learning, since ignoring either source of complexity can induce spurious causal relations among variables of interest. We study causal structure learning in linear systems where both challenges may occur simultaneously. We introduce a causal model called LV-SEM-ME, which contains four types of variables: directly observed variables, variables that are not directly observed but are measured with error, the corresponding measurements, and variables that are neither observed nor measured. Under a separability condition-namely, identifiability of the mixing matrix associated with the exogenous noise terms of the observed variables-together with certain faithfulness assumptions, we characterize the extent of identifiability and the corresponding observational equivalence classes. We provide graphical characterizations of these equivalence classes and develop recovery algorithms that enumerate all models in the equivalence class of the ground truth. We also establish, via a four-node union model that subsumes instrumental variable, front-door, and negative-control-outcome settings, a form of identification robustness: the target effect remains identifiable in the broader LV-SEM-ME model even when the assumptions underlying the specialized identification formulas for the corresponding submodels need not all hold simultaneously. Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI); Machine Learning (stat.ML) Cite as: arXiv:2407.19426 [cs.LG] (or arXiv:2407.19426v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2407.19426 Focus to learn more arXiv-issued DOI via DataCite Submission history From: AmirEmad Ghassami [ view email ] [v1] Sun, 28 Jul 2024 08:26:56 UTC (1,448 KB) [v2] Thu, 9 Apr 2026 02:18:18 UTC (63 KB) Full-text links: Access Paper: View a PDF of the paper titled Causal Discovery in Linear Models with Unobserved Variables and Measurement Error, by Yuqin Yang and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2024-07 Change to browse by: cs cs.AI stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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