mlsanityData to 14 Oct 2026

Identification of Nonlinear Latent Hierarchical Models

arXiv 2306.07916 ↗First posted 13 Jun 2023cs.LG cs.AI stat.MLcited by 27

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Abstract (arXiv)

Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be highly challenging, especially when observed variables are generated by causally related latent variables and the relationships are nonlinear. In this work, we investigate the identification problem for nonlinear latent hierarchical causal models in which observed variables are generated by a set of causally related latent variables, and some latent variables may not have observed children. We show that the identifiability of causal structures and latent variables (up to invertible transformations) can be achieved under mild assumptions: on causal structures, we allow for multiple paths between any pair of variables in the graph, which relaxes latent tree assumptions in prior work; on structural functions, we permit general nonlinearity and multi-dimensional continuous variables, alleviating existing work's parametric assumptions. Specifically, we first develop an identification criterion in the form of novel identifiability guarantees for an elementary latent variable model. Leveraging this criterion, we show that both causal structures and latent variables of the hierarchical model can be identified asymptotically by explicitly constructing an estimation procedure. To the best of our knowledge, our work is the first to establish identifiability guarantees for both causal structures and latent variables in nonlinear latent hierarchical models.

Key facts. Cited by 27 papers in the map (data through 14 Oct 2026). Builds on 17 of its 48 references that are in the map. First posted on arXiv 13 Jun 2023.

Builds on

17 of 48 references.

References · 17

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  3. 2019Variational Autoencoders and Nonlinear ICA: A Unifying Frameworkcited by 503
  4. 2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 312
  5. 2018Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learningcited by 282
  6. 2021Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICAcited by 160
  7. 2021Learning Temporally Causal Latent Processes from General Temporal Datacited by 98
  8. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  9. 2022On the Identifiability of Nonlinear ICA: Sparsity and Beyondcited by 85
  10. 2021Learning latent causal graphs via mixture oraclescited by 55
  11. 2022Latent Hierarchical Causal Structure Discovery with Rank Constraintscited by 51
  12. 2021Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspectivecited by 37
5 more
  1. 2023Learning nonparametric latent causal graphs with unknown interventionscited by 34
  2. 2021Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Biascited by 29
  3. 2022Learning Latent Causal Dynamicscited by 13
  4. 2014Marginal likelihood and model selection for Gaussian latent tree and forest modelscited by 12
  5. 2014Guaranteed Scalable Learning of Latent Tree Modelscited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 8; 2025: 11; 2026: 5.

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  1. 2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
  2. 2023Identifying Representations for Intervention Extrapolationcited by 21
  3. 2024Learning Discrete Concepts in Latent Hierarchical Modelscited by 17
  4. 2024On the Identification of Temporally Causal Representation with Instantaneous Dependencecited by 16
  5. 2024Counterfactual Generation with Identifiability Guaranteescited by 13
  6. 2025Towards Interpretable Deep Generative Models via Causal Representation Learningcited by 13
  7. 2024Identifiability Guarantees for Causal Disentanglement from Purely Observational Datacited by 7
  8. 2025Learning General Causal Structures with Hidden Dynamic Process for Climate Analysiscited by 7
  9. 2024From Orthogonality to Dependency: Learning Disentangled Representation for Multi-Modal Time-Series Sensing Signalscited by 4
  10. 2025Modeling Unseen Environments with Language-guided Composable Causal Components in Reinforcement Learningcited by 4
  11. 2025The Third Pillar of Causal Analysis? A Measurement Perspective on Causal Representationscited by 4
  12. 2025The Robustness of Differentiable Causal Discovery in Misspecified Scenarioscited by 4
15 more
  1. 2023Learned Causal Method Predictioncited by 3
  2. 2024Differentiable Causal Discovery For Latent Hierarchical Causal Modelscited by 3
  3. 2024Nonstationary Time Series Forecasting via Unknown Distribution Adaptationcited by 2
  4. 2024Towards Generalizable Reinforcement Learning via Causality-Guided Self-Adaptive Representationscited by 2
  5. 2025Online Time Series Forecasting with Theoretical Guaranteescited by 2
  6. 2025Time Series Domain Adaptation via Latent Invariant Causal Mechanismcited by 1
  7. 2025Causal View of Time Series Imputation: Some Identification Results on Missing Mechanismcited by 1
  8. 2025Learning by Analogy: A Causal Framework for Composition Generalizationcited by 1
  9. 2026Hierarchical Action Learning for Weakly-Supervised Action Segmentationcited by 1
  10. 2026Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixingcited by 1
  11. 2025Causal Representation Learning from Network Datacited by 0
  12. 2025Beyond the Black Box: Identifiable Interpretation and Control in Generative Models via Causal Minimalitycited by 0
  13. 2026Diverse Dictionary Learningcited by 0
  14. 2026Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Modelscited by 0
  15. 2026Towards Identifiable Representations under Misspecified Structurecited by 0