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Latent Hierarchical Causal Structure Discovery with Rank Constraints

arXiv 2210.01798 ↗First posted 1 Oct 2022cs.LG cs.AIcited by 50

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Abstract (arXiv)

Most causal discovery procedures assume that there are no latent confounders in the system, which is often violated in real-world problems. In this paper, we consider a challenging scenario for causal structure identification, where some variables are latent and they form a hierarchical graph structure to generate the measured variables; the children of latent variables may still be latent and only leaf nodes are measured, and moreover, there can be multiple paths between every pair of variables (i.e., it is beyond tree structure). We propose an estimation procedure that can efficiently locate latent variables, determine their cardinalities, and identify the latent hierarchical structure, by leveraging rank deficiency constraints over the measured variables. We show that the proposed algorithm can find the correct Markov equivalence class of the whole graph asymptotically under proper restrictions on the graph structure.

Key facts. Cited by 50 papers in the map (data through 7 Oct 2026). Builds on 11 of its 48 references that are in the map. First posted on arXiv 1 Oct 2022.

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11 of 48 references.

References · 11

  1. 2019Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changescited by 166
  2. 2021Learning latent causal graphs via mixture oraclescited by 55
  3. 2019Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variablescited by 39
  4. 2013ParceLiNGAM: A causal ordering method robust against latent confounderscited by 29
  5. 2021Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Biascited by 29
  6. 2022Causal Structure Discovery between Clusters of Nodes Induced by Latent Factorscited by 18
  7. 2017Robust causal structure learning with some hidden variablescited by 17
  8. 2020Causal Discovery with Multi-Domain LiNGAM for Latent Factorscited by 13
  9. 2013Calculation of Entailed Rank Constraints in Partially Non-Linear and Cyclic Modelscited by 12
  10. 2014Marginal likelihood and model selection for Gaussian latent tree and forest modelscited by 12
  11. 2020Causal Clustering for 1-Factor Measurement Models on Data with Various Typescited by 2

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Citing papers per year: 2023: 14; 2024: 15; 2025: 11; 2026: 10.

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  1. 2024Causal Representation Learning from Multiple Distributions: A General Settingcited by 67
  2. 2023Understanding Masked Autoencoders via Hierarchical Latent Variable Modelscited by 39
  3. 2023Learning nonparametric latent causal graphs with unknown interventionscited by 34
  4. 2023A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variablescited by 33
  5. 2023Unpaired Multi-Domain Causal Representation Learningcited by 32
  6. 2023Identification of Nonlinear Latent Hierarchical Modelscited by 27
  7. 2023Identifiable Latent Polynomial Causal Models Through the Lens of Changecited by 23
  8. 2024CaRiNG: Learning Temporal Causal Representation under Non-Invertible Generation Processcited by 20
  9. 2024Learning Discrete Concepts in Latent Hierarchical Modelscited by 17
  10. 2024On the Identification of Temporally Causal Representation with Instantaneous Dependencecited by 15
  11. 2024Causal Temporal Representation Learning with Nonstationary Sparse Transitioncited by 12
  12. 2025Towards Interpretable Deep Generative Models via Causal Representation Learningcited by 12
38 more
  1. 2023Emerging Synergies in Causality and Deep Generative Models: A Surveycited by 10
  2. 2023Identification of Causal Structure with Latent Variables Based on Higher Order Cumulantscited by 8
  3. 2024On the Parameter Identifiability of Partially Observed Linear Causal Modelscited by 7
  4. 2024A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discoverycited by 7
  5. 2025Debiasing Reward Models by Representation Learning with Guaranteescited by 6
  6. 2025Latent Variable Causal Discovery under Selection Biascited by 6
  7. 2024Towards Identifiable Latent Additive Noise Modelscited by 5
  8. 2024Identifiability Analysis of Linear ODE Systems with Hidden Confounderscited by 5
  9. 2023Neuro-Causal Factor Analysiscited by 4
  10. 2023Towards Characterizing Domain Counterfactuals For Invertible Latent Causal Modelscited by 4
  11. 2024Long-Term Fairness Inquiries and Pursuits in Machine Learning: A Survey of Notions, Methods, and Challengescited by 4
  12. 2025Permutation-Based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Datacited by 4
  13. 2026Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learningcited by 4
  14. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 4
  15. 2023s-ID: Causal Effect Identification in a Sub-Populationcited by 3
  16. 2023Causal Discovery in Mixtures of Populationscited by 3
  17. 2024Learning Discrete Latent Variable Structures with Tensor Rank Conditionscited by 3
  18. 2024Differentiable Causal Discovery For Latent Hierarchical Causal Modelscited by 3
  19. 2025CausalVerse: Benchmarking Causal Representation Learning with Configurable High-Fidelity Simulationscited by 3
  20. 2023On the Unlikelihood of D-Separationcited by 2
  21. 2024Automating the Selection of Proxy Variables of Unmeasured Confounderscited by 2
  22. 2026A General Representation-Based Approach to Multi-Source Domain Adaptationcited by 2
  23. 2026Score-Based Causal Discovery of Latent Variable Causal Modelscited by 2
  24. 2023On the Three Demons in Causality in Finance: Time Resolution, Nonstationarity, and Latent Factorscited by 1
  25. 2024Structural Disentanglement of Causal and Correlated Conceptscited by 1
  26. 2025Evolved Hierarchical Masking for Self-Supervised Learningcited by 1
  27. 2025Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Modelscited by 1
  28. 2025Learning by Analogy: A Causal Framework for Composition Generalizationcited by 1
  29. 2026Traceable Latent Variable Discovery Based on Multi-Agent Collaborationcited by 1
  30. 2024Continual Learning of Nonlinear Independent Representationscited by 0
  31. 2025On Theoretical Identifiability of Discrete Latent Causal Graphical Modelscited by 0
  32. 2025Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networkscited by 0
  33. 2025Beyond the Black Box: Identifiable Interpretation and Control in Generative Models via Causal Minimalitycited by 0
  34. 2026Efficient Causal Structure Learning via Modular Subgraph Integrationcited by 0
  35. 2026Beyond identifiability: Learning causal representations with few environments and finite samplescited by 0
  36. 2026Discrete Causal Representations from Heterogeneous Domains: A Bayesian Approach with Social Survey Applicationscited by 0
  37. 2026Provable Guarantees and Efficient Learning of Structural Equation Models with Latent Confounderscited by 0
  38. 2026Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Modelscited by 0