mlsanityData to 7 Oct 2026

Learning nonparametric latent causal graphs with unknown interventions

arXiv 2306.02899 ↗First posted 5 Jun 2023stat.ML cs.LGcited by 34

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Abstract (arXiv)

We establish conditions under which latent causal graphs are nonparametrically identifiable and can be reconstructed from unknown interventions in the latent space. Our primary focus is the identification of the latent structure in measurement models without parametric assumptions such as linearity or Gaussianity. Moreover, we do not assume the number of hidden variables is known, and we show that at most one unknown intervention per hidden variable is needed. This extends a recent line of work on learning causal representations from observations and interventions. The proofs are constructive and introduce two new graphical concepts -- imaginary subsets and isolated edges -- that may be useful in their own right. As a matter of independent interest, the proofs also involve a novel characterization of the limits of edge orientations within the equivalence class of DAGs induced by unknown interventions. These are the first results to characterize the conditions under which causal representations are identifiable without making any parametric assumptions in a general setting with unknown interventions and without faithfulness.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). Builds on 35 of its 112 references that are in the map. First posted on arXiv 5 Jun 2023.

Builds on

35 of 112 references.

References · 35

  1. 2019Variational Autoencoders and Nonlinear ICA: A Unifying Frameworkcited by 494
  2. 2015MADE: Masked Autoencoder for Distribution Estimationcited by 306
  3. 2016Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICAcited by 270
  4. 2021Contrastive Learning Inverts the Data Generating Processcited by 220
  5. 2021Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICAcited by 158
  6. 2017CausalGAN: Learning Causal Implicit Generative Models with Adversarial Trainingcited by 152
  7. 2022Weakly supervised causal representation learningcited by 140
  8. 2022Interventional Causal Representation Learningcited by 140
  9. 2022CITRIS: Causal Identifiability from Temporal Intervened Sequencescited by 132
  10. 2016Composing graphical models with neural networks for structured representations and fast inferencecited by 113
  11. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
  12. 2020On Linear Identifiability of Learned Representationscited by 103
23 more
  1. 2020ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICAcited by 102
  2. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  3. 2020Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)cited by 91
  4. 2022Linear Causal Disentanglement via Interventionscited by 84
  5. 2018Characterizing and Learning Equivalence Classes of Causal DAGs under Interventionscited by 76
  6. 2019Permutation-Based Causal Structure Learning with Unknown Intervention Targetscited by 69
  7. 2021Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICAcited by 64
  8. 2014Visual Causal Feature Learningcited by 59
  9. 2023Posterior Collapse and Latent Variable Non-identifiabilitycited by 57
  10. 2021Learning latent causal graphs via mixture oraclescited by 55
  11. 2022Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesiscited by 54
  12. 2013Causal Discovery from Changescited by 52
  13. 2022Latent Hierarchical Causal Structure Discovery with Rank Constraintscited by 50
  14. 2023Score-based Causal Representation Learning with Interventionscited by 49
  15. 2013A Transformational Characterization of Equivalent Bayesian Network Structurescited by 41
  16. 2017Faithful Inversion of Generative Models for Effective Amortized Inferencecited by 28
  17. 2022BaCaDI: Bayesian Causal Discovery with Unknown Interventionscited by 26
  18. 2022Differentiable Causal Discovery Under Latent Interventionscited by 21
  19. 2019Measurement Dependence Inducing Latent Causal Modelscited by 14
  20. 2015Anchored Discrete Factor Analysiscited by 9
  21. 2019Identifying through Flows for Recovering Latent Representationscited by 8
  22. 2015Learning from Pairwise Marginal Independenciescited by 5
  23. 2022Combinatorial and algebraic perspectives on the marginal independence structure of Bayesian networkscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 8; 2024: 10; 2025: 7; 2026: 9.

34 papers.

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  1. 2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
  2. 2024Causal Representation Learning from Multiple Distributions: A General Settingcited by 67
  3. 2023Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolationcited by 56
  4. 2023General Identifiability and Achievability for Causal Representation Learningcited by 34
  5. 2025Thought Communication in Multiagent Collaborationcited by 28
  6. 2023Identification of Nonlinear Latent Hierarchical Modelscited by 27
  7. 2023Multi-Domain Causal Representation Learning via Weak Distributional Invariancescited by 23
  8. 2023Identifying Representations for Intervention Extrapolationcited by 21
  9. 2024Linear Causal Representation Learning from Unknown Multi-node Interventionscited by 14
  10. 2024Causal Representation Learning from Multimodal Biomedical Observationscited by 12
  11. 2025Towards Interpretable Deep Generative Models via Causal Representation Learningcited by 12
  12. 2023An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysiscited by 9
22 more
  1. 2024Automated Discovery of Pairwise Interactions from Unstructured Datacited by 8
  2. 2024Identifiability Guarantees for Causal Disentanglement from Purely Observational Datacited by 7
  3. 2025Debiasing Reward Models by Representation Learning with Guaranteescited by 6
  4. 2024Toward the Identifiability of Comparative Deep Generative Modelscited by 4
  5. 2024Sample Efficient Bayesian Learning of Causal Graphs from Interventionscited by 4
  6. 2024Identifying General Mechanism Shifts in Linear Causal Representationscited by 4
  7. 2026Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learningcited by 4
  8. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 4
  9. 2024Lambda: Learning Matchable Prior For Entity Alignment with Unlabeled Dangling Casescited by 3
  10. 2025Mechanistic Independence: A Principle for Identifiable Disentangled Representationscited by 3
  11. 2025Characterization and Learning of Causal Graphs from Hard Interventionscited by 2
  12. 2026Coarsening Causal DAG Modelscited by 2
  13. 2026Causal Representation Meets Stochastic Modeling under Generic Geometrycited by 2
  14. 2026A General Representation-Based Approach to Multi-Source Domain Adaptationcited by 2
  15. 2023A Review and Roadmap of Deep Causal Model from Different Causal Structures and Representationscited by 1
  16. 2024Linear causal disentanglement via higher-order cumulantscited by 1
  17. 2025Feature Matching Intervention: Leveraging Observational Data for Causal Representation Learningcited by 0
  18. 2025Incorporating Interventional Independence Improves Robustness against Interventional Distribution Shiftcited by 0
  19. 2026Beyond identifiability: Learning causal representations with few environments and finite samplescited by 0
  20. 2026Diverse Dictionary Learningcited by 0
  21. 2026From Generalist to Specialist Representationcited by 0
  22. 2026Identification of Nonlinear and Dependent Latent Factor Structure through Clique Searchcited by 0