mlsanityData to 14 Oct 2026

Learning latent causal graphs via mixture oracles

arXiv 2106.15563 ↗First posted 29 Jun 2021cs.LG cs.AI stat.MLcited by 55

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Abstract (arXiv)

We study the problem of reconstructing a causal graphical model from data in the presence of latent variables. The main problem of interest is recovering the causal structure over the latent variables while allowing for general, potentially nonlinear dependence between the variables. In many practical problems, the dependence between raw observations (e.g. pixels in an image) is much less relevant than the dependence between certain high-level, latent features (e.g. concepts or objects), and this is the setting of interest. We provide conditions under which both the latent representations and the underlying latent causal model are identifiable by a reduction to a mixture oracle. These results highlight an intriguing connection between the well-studied problem of learning the order of a mixture model and the problem of learning the bipartite structure between observables and unobservables. The proof is constructive, and leads to several algorithms for explicitly reconstructing the full graphical model. We discuss efficient algorithms and provide experiments illustrating the algorithms in practice.

Key facts. Cited by 55 papers in the map (data through 14 Oct 2026). Builds on 28 of its 99 references that are in the map. First posted on arXiv 29 Jun 2021.

Builds on

28 of 99 references.

References · 28

  1. 2019Variational Autoencoders and Nonlinear ICA: A Unifying Frameworkcited by 503
  2. 2018Neural Relational Inference for Interacting Systemscited by 339
  3. 2013Causal Discovery with Continuous Additive Noise Modelscited by 255
  4. 2013Causal Inference in the Presence of Latent Variables and Selection Biascited by 166
  5. 2017CausalGAN: Learning Causal Implicit Generative Models with Adversarial Trainingcited by 152
  6. 2016Discovering Causal Signals in Imagescited by 79
  7. 2020Causal Discovery in Physical Systems from Videoscited by 77
  8. 2014Visual Causal Feature Learningcited by 59
  9. 2017Pixels to Graphs by Associative Embeddingcited by 58
  10. 2019Causal Discovery with General Non-Linear Relationships Using Non-Linear ICAcited by 58
  11. 2017Nested Markov Properties for Acyclic Directed Mixed Graphscited by 39
  12. 2020A polynomial-time algorithm for learning nonparametric causal graphscited by 30
16 more
  1. 2015Margins of discrete Bayesian networkscited by 26
  2. 2019On Multi-Cause Causal Inference with Unobserved Confounding: Counterexamples, Impossibility, and Alternativescited by 20
  3. 2017Robust causal structure learning with some hidden variablescited by 17
  4. 2018Identifiability of Nonparametric Mixture Models and Bayes Optimal Clusteringcited by 15
  5. 2019Measurement Dependence Inducing Latent Causal Modelscited by 14
  6. 2013Markovian acyclic directed mixed graphs for discrete datacited by 10
  7. 2015A Uniformly Consistent Estimator of Causal Effects under the k-Triangle-Faithfulness Assumptioncited by 10
  8. 2018Learning Restricted Boltzmann Machines via Influence Maximizationcited by 10
  9. 2015Smooth, identifiable supermodels of discrete DAG models with latent variablescited by 8
  10. 2020Estimating the Number of Components in Finite Mixture Models via the Group-Sort-Fuse Procedurecited by 8
  11. 2020Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observationscited by 8
  12. 2020Na"ive regression requires weaker assumptions than factor models to adjust for multiple cause confoundingcited by 5
  13. 2021Hadamard Extensions and the Identification of Mixtures of Product Distributionscited by 4
  14. 2013Finite state space non parametric Hidden Markov Models are in general identifiablecited by 2
  15. 2018Smoothed Analysis of Discrete Tensor Decomposition and Assemblies of Neuronscited by 2
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 8; 2023: 15; 2024: 12; 2025: 9; 2026: 9.

55 papers.

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  1. 2022Weakly supervised causal representation learningcited by 140
  2. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 106
  3. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  4. 2022Linear Causal Disentanglement via Interventionscited by 84
  5. 2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
  6. 2024On the Origins of Linear Representations in Large Language Modelscited by 79
  7. 2023Multi-View Causal Representation Learning with Partial Observabilitycited by 74
  8. 2022Identifiability of deep generative models without auxiliary informationcited by 70
  9. 2024Causal Representation Learning from Multiple Distributions: A General Settingcited by 68
  10. 2022Latent Hierarchical Causal Structure Discovery with Rank Constraintscited by 51
  11. 2022Causal Structure Learning: a Combinatorial Perspectivecited by 46
  12. 2024A Sparsity Principle for Partially Observable Causal Representation Learningcited by 35
38 more
  1. 2022Identifying Weight-Variant Latent Causal Modelscited by 34
  2. 2023Learning nonparametric latent causal graphs with unknown interventionscited by 34
  3. 2023A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variablescited by 33
  4. 2023Causal Representation Learning Made Identifiable by Grouping of Observational Variablescited by 32
  5. 2024Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Modelscited by 29
  6. 2023Identification of Nonlinear Latent Hierarchical Modelscited by 27
  7. 2023Identifying Representations for Intervention Extrapolationcited by 21
  8. 2024Learning Discrete Concepts in Latent Hierarchical Modelscited by 17
  9. 2025I Predict Therefore I Am: Is Next Token Prediction Enough to Learn Human-Interpretable Concepts from Data?cited by 13
  10. 2025Towards Interpretable Deep Generative Models via Causal Representation Learningcited by 13
  11. 2024Smoke and Mirrors in Causal Downstream Taskscited by 12
  12. 2024Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environmentcited by 12
  13. 2021Causal Inference Despite Limited Global Confounding via Mixture Modelscited by 9
  14. 2023An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysiscited by 9
  15. 2023Tier Balancing: Towards Dynamic Fairness over Underlying Causal Factorscited by 7
  16. 2024A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discoverycited by 7
  17. 2024Identifiability Guarantees for Causal Disentanglement from Purely Observational Datacited by 7
  18. 2025Latent Variable Causal Discovery under Selection Biascited by 7
  19. 2025What is causal about causal models and representations?cited by 6
  20. 2025Debiasing Reward Models by Representation Learning with Guaranteescited by 6
  21. 2021Uniform Consistency in Nonparametric Mixture Modelscited by 5
  22. 2022Learning Latent Structural Causal Modelscited by 5
  23. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 5
  24. 2023Entity Aware Modelling: A Surveycited by 4
  25. 2023Neuro-Causal Factor Analysiscited by 4
  26. 2025CausalVerse: Benchmarking Causal Representation Learning with Configurable High-Fidelity Simulationscited by 4
  27. 2026Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learningcited by 4
  28. 2022Tight Bounds on the Hardness of Learning Simple Nonparametric Mixturescited by 3
  29. 2024Learning Discrete Latent Variable Structures with Tensor Rank Conditionscited by 3
  30. 2024Differentiable Causal Discovery For Latent Hierarchical Causal Modelscited by 3
  31. 2026Score-Based Causal Discovery of Latent Variable Causal Modelscited by 3
  32. 2025Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Modelscited by 2
  33. 2026A General Representation-Based Approach to Multi-Source Domain Adaptationcited by 2
  34. 2023On the Three Demons in Causality in Finance: Time Resolution, Nonstationarity, and Latent Factorscited by 1
  35. 2024Linear causal disentanglement via higher-order cumulantscited by 1
  36. 2026Traceable Latent Variable Discovery Based on Multi-Agent Collaborationcited by 1
  37. 2026Beyond identifiability: Learning causal representations with few environments and finite samplescited by 1
  38. 2023Scalable Clustering: Large Scale Unsupervised Learning of Gaussian Mixture Models with Outlierscited by 0

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