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On Theoretical Identifiability of Discrete Latent Causal Graphical Models

arXiv 2505.18410 ↗First posted 23 May 2025stat.ML cs.LGcited by 0

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Abstract (arXiv)

This paper considers a challenging problem of identifying a causal graphical model under the presence of latent variables. While various identifiability conditions have been proposed in the literature, they often require multiple pure children per latent variable or restrictions on the latent causal graph. Furthermore, it is common for all observed variables to exhibit the same modality. Consequently, the existing identifiability conditions are often too stringent for complex real-world data. We consider a general nonparametric measurement model with arbitrary observed variable types and binary latent variables, and propose a double triangular graphical condition that guarantees identifiability of the entire causal graphical model. The proposed condition significantly relaxes the popular pure children condition. We also establish necessary conditions for identifiability and provide valuable insights into fundamental limits of identifiability. Simulation studies verify that latent structures satisfying our conditions can be accurately estimated from data.

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References · 20

  1. 2021Learning latent causal graphs via mixture oraclescited by 55
  2. 2022Latent Hierarchical Causal Structure Discovery with Rank Constraintscited by 51
  3. 2023Causal Discovery with Score Matching on Additive Models with Arbitrary Noisecited by 43
  4. 2023A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variablescited by 33
  5. 2015Margins of discrete Bayesian networkscited by 26
  6. 2017Robust causal structure learning with some hidden variablescited by 17
  7. 2024Learning Discrete Concepts in Latent Hierarchical Modelscited by 17
  8. 2021Bayesian Pyramids: Identifiable Multilayer Discrete Latent Structure Models for Discrete Datacited by 16
  9. 2019Measurement Dependence Inducing Latent Causal Modelscited by 14
  10. 2025Towards Interpretable Deep Generative Models via Causal Representation Learningcited by 13
  11. 2023Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variablescited by 11
  12. 2024Demystifying amortized causal discovery with transformerscited by 11
8 more
  1. 2021Causal Inference Despite Limited Global Confounding via Mixture Modelscited by 9
  2. 2022Blessing of Dependence: Identifiability and Geometry of Discrete Models with Multiple Binary Latent Variablescited by 5
  3. 2024Learning Discrete Latent Variable Structures with Tensor Rank Conditionscited by 3
  4. 2014Nonparametric Latent Tree Graphical Models: Inference, Estimation, and Structure Learningcited by 2
  5. 2021Learning Latent and Hierarchical Structures in Cognitive Diagnosis Modelscited by 2
  6. 2023Latent Conjunctive Bayesian Network: Unify Attribute Hierarchy and Bayesian Network for Cognitive Diagnosiscited by 2
  7. 2025Deep Discrete Encoders: Identifiable Deep Generative Models for Rich Data with Discrete Latent Layerscited by 2
  8. 2021Identifiability of Latent Class Models with Covariatescited by 1

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