mlsanityData to 7 Oct 2026

Score-based Causal Representation Learning with Interventions

arXiv 2301.08230 ↗First posted 19 Jan 2023stat.ML cs.LGcited by 49

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Abstract (arXiv)

This paper studies the causal representation learning problem when the latent causal variables are observed indirectly through an unknown linear transformation. The objectives are: (i) recovering the unknown linear transformation (up to scaling) and (ii) determining the directed acyclic graph (DAG) underlying the latent variables. Sufficient conditions for DAG recovery are established, and it is shown that a large class of non-linear models in the latent space (e.g., causal mechanisms parameterized by two-layer neural networks) satisfy these conditions. These sufficient conditions ensure that the effect of an intervention can be detected correctly from changes in the score. Capitalizing on this property, recovering a valid transformation is facilitated by the following key property: any valid transformation renders latent variables' score function to necessarily have the minimal variations across different interventional environments. This property is leveraged for perfect recovery of the latent DAG structure using only soft interventions. For the special case of stochastic hard interventions, with an additional hypothesis testing step, one can also uniquely recover the linear transformation up to scaling and a valid causal ordering.

Key facts. Cited by 49 papers in the map (data through 7 Oct 2026). Builds on 33 of its 53 references that are in the map. First posted on arXiv 19 Jan 2023.

Builds on

33 of 53 references.

References · 33

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 929
  4. 2021Score-based Generative Modeling in Latent Spacecited by 634
  5. 2018Disentangling by Factorisingcited by 614
  6. 2019Variational Autoencoders and Nonlinear ICA: A Unifying Frameworkcited by 494
  7. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  8. 2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 308
  9. 2021Score-based diffusion models for accelerated MRIcited by 308
  10. 2018Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learningcited by 278
  11. 2019Causality for Machine Learningcited by 242
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21 more
  1. 2020Weakly-Supervised Disentanglement Without Compromisescited by 237
  2. 2021Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICAcited by 158
  3. 2022Weakly supervised causal representation learningcited by 140
  4. 2022Interventional Causal Representation Learningcited by 140
  5. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
  6. 2020ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICAcited by 102
  7. 2021Learning Temporally Causal Latent Processes from General Temporal Datacited by 96
  8. 2022Linear Causal Disentanglement via Interventionscited by 84
  9. 2019Weakly Supervised Disentanglement with Guaranteescited by 82
  10. 2018Characterizing and Learning Equivalence Classes of Causal DAGs under Interventionscited by 76
  11. 2020Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Seriescited by 76
  12. 2022Weakly Supervised Representation Learning with Sparse Perturbationscited by 64
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  14. 2022Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesiscited by 54
  15. 2022From Statistical to Causal Learningcited by 40
  16. 2020On Implicit Regularization in β-VAEscited by 34
  17. 2022Identifying Weight-Variant Latent Causal Modelscited by 33
  18. 2021Properties from Mechanisms: An Equivariance Perspective on Identifiable Representation Learningcited by 30
  19. 2021Causal Reasoning in Simulation for Structure and Transfer Learning of Robot Manipulation Policiescited by 20
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  21. 2022Learning by Doing: Controlling a Dynamical System using Causality, Control, and Reinforcement Learningcited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 17; 2024: 13; 2025: 12; 2026: 7.

49 papers.

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  1. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
  2. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  3. 2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
  4. 2024On the Origins of Linear Representations in Large Language Modelscited by 76
  5. 2023Multi-View Causal Representation Learning with Partial Observabilitycited by 72
  6. 2024Causal Representation Learning from Multiple Distributions: A General Settingcited by 67
  7. 2023Causal Component Analysiscited by 56
  8. 2023Learning nonparametric latent causal graphs with unknown interventionscited by 34
  9. 2023General Identifiability and Achievability for Causal Representation Learningcited by 34
  10. 2023Causal Representation Learning Made Identifiable by Grouping of Observational Variablescited by 30
  11. 2024Unifying Causal Representation Learning with the Invariance Principlecited by 30
  12. 2024Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Modelscited by 29
37 more
  1. 2023Multi-Domain Causal Representation Learning via Weak Distributional Invariancescited by 23
  2. 2023Identifiable Latent Polynomial Causal Models Through the Lens of Changecited by 23
  3. 2023Identifying Representations for Intervention Extrapolationcited by 21
  4. 2023Identifying Linearly-Mixed Causal Representations from Multi-Node Interventionscited by 18
  5. 2023Learning Causal Representations from General Environments: Identifiability and Intrinsic Ambiguitycited by 14
  6. 2024Linear Causal Representation Learning from Unknown Multi-node Interventionscited by 14
  7. 2025I Predict Therefore I Am: Is Next Token Prediction Enough to Learn Human-Interpretable Concepts from Data?cited by 13
  8. 2024Smoke and Mirrors in Causal Downstream Taskscited by 12
  9. 2024Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environmentcited by 12
  10. 2024Causal Representation Learning from Multimodal Biomedical Observationscited by 12
  11. 2025Towards Interpretable Deep Generative Models via Causal Representation Learningcited by 12
  12. 2024Beyond DAGs: A Latent Partial Causal Model for Multimodal Learningcited by 9
  13. 2024Identifiability Guarantees for Causal Disentanglement from Purely Observational Datacited by 7
  14. 2025Robustness of Nonlinear Representation Learningcited by 7
  15. 2025Debiasing Reward Models by Representation Learning with Guaranteescited by 6
  16. 2023Invariance & Causal Representation Learning: Prospects and Limitationscited by 5
  17. 2024Towards Identifiable Latent Additive Noise Modelscited by 5
  18. 2025Sanity Checking Causal Representation Learning on a Simple Real-World Systemcited by 5
  19. 2023Neuro-Causal Factor Analysiscited by 4
  20. 2023Towards Characterizing Domain Counterfactuals For Invertible Latent Causal Modelscited by 4
  21. 2024Identifying General Mechanism Shifts in Linear Causal Representationscited by 4
  22. 2025Exploratory Causal Inference in SAEncecited by 4
  23. 2026Structural Causal Bottleneck Modelscited by 4
  24. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 4
  25. 2023A Causal Ordering Prior for Unsupervised Representation Learningcited by 3
  26. 2026A General Representation-Based Approach to Multi-Source Domain Adaptationcited by 2
  27. 2024Linear causal disentanglement via higher-order cumulantscited by 1
  28. 2025Causal Representation Learning with Observational Grouping for CXR Classificationcited by 1
  29. 2025Intervening to Learn and Compose Causally Disentangled Representationscited by 1
  30. 2026Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixingcited by 1
  31. 2025Incorporating Interventional Independence Improves Robustness against Interventional Distribution Shiftcited by 0
  32. 2025Learning Robust Intervention Representations with Delta Embeddingscited by 0
  33. 2025Causal Representation Learning from Network Datacited by 0
  34. 2025Linear Causal Representation Learning by Topological Ordering, Pruning, and Disentanglementcited by 0
  35. 2026Concept Component Analysis: A Principled Approach for Concept Extraction in LLMscited by 0
  36. 2026Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Modelscited by 0
  37. 2026I Act Therefore I Am: When Is JEPA's Action-Conditioning Enough to Learn Causal Mechanisms?cited by 0