mlsanityData to 14 Oct 2026

Causal Component Analysis

arXiv 2305.17225 ↗First posted 26 May 2023stat.ML cs.AI cs.LGcited by 56

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Abstract (arXiv)

Independent Component Analysis (ICA) aims to recover independent latent variables from observed mixtures thereof. Causal Representation Learning (CRL) aims instead to infer causally related (thus often statistically dependent) latent variables, together with the unknown graph encoding their causal relationships. We introduce an intermediate problem termed Causal Component Analysis (CauCA). CauCA can be viewed as a generalization of ICA, modelling the causal dependence among the latent components, and as a special case of CRL. In contrast to CRL, it presupposes knowledge of the causal graph, focusing solely on learning the unmixing function and the causal mechanisms. Any impossibility results regarding the recovery of the ground truth in CauCA also apply for CRL, while possibility results may serve as a stepping stone for extensions to CRL. We characterize CauCA identifiability from multiple datasets generated through different types of interventions on the latent causal variables. As a corollary, this interventional perspective also leads to new identifiability results for nonlinear ICA -- a special case of CauCA with an empty graph -- requiring strictly fewer datasets than previous results. We introduce a likelihood-based approach using normalizing flows to estimate both the unmixing function and the causal mechanisms, and demonstrate its effectiveness through extensive synthetic experiments in the CauCA and ICA setting.

Key facts. Cited by 56 papers in the map (data through 14 Oct 2026). Builds on 39 of its 68 references that are in the map. First posted on arXiv 26 May 2023.

Builds on

39 of 68 references.

References · 39

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  3. 2019Neural Spline Flowscited by 596
  4. 2019Variational Autoencoders and Nonlinear ICA: A Unifying Frameworkcited by 503
  5. 2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 312
  6. 2018Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learningcited by 282
  7. 2016Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICAcited by 273
  8. 2020Weakly-Supervised Disentanglement Without Compromisescited by 239
  9. 2021Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICAcited by 160
  10. 2022Interventional Causal Representation Learningcited by 142
  11. 2022Weakly supervised causal representation learningcited by 140
  12. 2022CITRIS: Causal Identifiability from Temporal Intervened Sequencescited by 133
27 more
  1. 2021Counterfactual Generative Networkscited by 111
  2. 2020ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICAcited by 102
  3. 2021Learning Temporally Causal Latent Processes from General Temporal Datacited by 98
  4. 2021Independent mechanism analysis, a new concept?cited by 97
  5. 2020On Disentangled Representations Learned From Correlated Datacited by 94
  6. 2019The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICAcited by 86
  7. 2022Linear Causal Disentanglement via Interventionscited by 84
  8. 2020Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Seriescited by 77
  9. 2021Desiderata for Representation Learning: A Causal Perspectivecited by 76
  10. 2022Identifiability of deep generative models without auxiliary informationcited by 70
  11. 2020Weakly Supervised Disentangled Generative Causal Representation Learningcited by 68
  12. 2022Weakly Supervised Representation Learning with Sparse Perturbationscited by 65
  13. 2021Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICAcited by 64
  14. 2023Identifiability Results for Multimodal Contrastive Learningcited by 61
  15. 2019Causal Discovery with General Non-Linear Relationships Using Non-Linear ICAcited by 58
  16. 2023Identifiability of latent-variable and structural-equation models: from linear to nonlinearcited by 58
  17. 2022Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesiscited by 55
  18. 2022Function Classes for Identifiable Nonlinear Independent Component Analysiscited by 53
  19. 2022Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systemscited by 51
  20. 2023Score-based Causal Representation Learning with Interventionscited by 49
  21. 2020CausalVAE: Structured Causal Disentanglement in Variational Autoencodercited by 48
  22. 2021Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspectivecited by 37
  23. 2022Indeterminacy in Generative Models: Characterization and Strong Identifiabilitycited by 33
  24. 2021Unsupervised Object Learning via Common Fatecited by 29
  25. 2022Partial Disentanglement via Mechanism Sparsitycited by 29
  26. 2020Relative gradient optimization of the Jacobian term in unsupervised deep learningcited by 16
  27. 2020Structure by Architecture: Structured Representations without Regularizationcited by 10

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 13; 2024: 15; 2025: 19; 2026: 9.

56 papers.

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  1. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 106
  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. 2023Multi-View Causal Representation Learning with Partial Observabilitycited by 74
  5. 2023Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcutscited by 63
  6. 2023Provable Compositional Generalization for Object-Centric Learningcited by 41
  7. 2024BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcutscited by 37
  8. 2024A Sparsity Principle for Partially Observable Causal Representation Learningcited by 35
  9. 2023General Identifiability and Achievability for Causal Representation Learningcited by 34
  10. 2024Unifying Causal Representation Learning with the Invariance Principlecited by 31
  11. 2023Multi-Domain Causal Representation Learning via Weak Distributional Invariancescited by 23
  12. 2024Interaction Asymmetry: A General Principle for Learning Composable Abstractionscited by 20
38 more
  1. 2024A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcutscited by 19
  2. 2023Identifying Linearly-Mixed Causal Representations from Multi-Node Interventionscited by 18
  3. 2024On the Identification of Temporally Causal Representation with Instantaneous Dependencecited by 16
  4. 2023Targeted Reduction of Causal Modelscited by 15
  5. 2023Learning Causally Disentangled Representations via the Principle of Independent Causal Mechanismscited by 14
  6. 2024All or None: Identifiable Linear Properties of Next-token Predictors in Language Modelingcited by 14
  7. 2024Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environmentcited by 12
  8. 2023Deep Backtracking Counterfactuals for Causally Compliant Explanationscited by 9
  9. 2023An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysiscited by 9
  10. 2025Position: An Empirically Grounded Identifiability Theory Will Accelerate Self-Supervised Learning Researchcited by 9
  11. 2024Identifiability Guarantees for Causal Disentanglement from Purely Observational Datacited by 7
  12. 2025From Isolation to Entanglement: When Do Interpretability Methods Identify and Disentangle Known Concepts?cited by 7
  13. 2025What is causal about causal models and representations?cited by 6
  14. 2025Debiasing Reward Models by Representation Learning with Guaranteescited by 6
  15. 2024Towards Identifiable Latent Additive Noise Modelscited by 5
  16. 2024Half-VAE: An Encoder-Free VAE to Bypass Explicit Inverse Mappingcited by 5
  17. 2025Sanity Checking Causal Representation Learning on a Simple Real-World Systemcited by 5
  18. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 5
  19. 2024From Orthogonality to Dependency: Learning Disentangled Representation for Multi-Modal Time-Series Sensing Signalscited by 4
  20. 2025The Third Pillar of Causal Analysis? A Measurement Perspective on Causal Representationscited by 4
  21. 2025When Does Closeness in Distribution Imply Representational Similarity? An Identifiability Perspectivecited by 4
  22. 2025Measure-Theoretic Anti-Causal Representation Learningcited by 4
  23. 2026Structural Causal Bottleneck Modelscited by 4
  24. 2024A Causal Framework for Precision Rehabilitationcited by 2
  25. 2025Structured Kernel Regression VAE: A Computationally Efficient Surrogate for GP-VAEs in ICAcited by 2
  26. 2026A General Representation-Based Approach to Multi-Source Domain Adaptationcited by 2
  27. 2024Identifiable Representation and Model Learning for Latent Dynamic Systemscited by 1
  28. 2025Time Series Domain Adaptation via Latent Invariant Causal Mechanismcited by 1
  29. 2025On the Identifiability of Causal Abstractionscited by 1
  30. 2025Causal View of Time Series Imputation: Some Identification Results on Missing Mechanismcited by 1
  31. 2025Towards Causal Representation Learning with Observable Sources as Auxiliariescited by 1
  32. 2026Hierarchical Action Learning for Weakly-Supervised Action Segmentationcited by 1
  33. 2026Multi-Domain Empirical Bayes for Linearly-Mixed Causal Representationscited by 1
  34. 2026Structure-agnostic Causal Representation Learningcited by 1
  35. 2024Disentangled Representations for Causal Cognitioncited by 0
  36. 2025Learning Joint Interventional Effects from Single-Variable Interventions in Additive Modelscited by 0
  37. 2025Estimating Treatment Effects with Independent Component Analysiscited by 0
  38. 2025Learning Robust Intervention Representations with Delta Embeddingscited by 0

50 most cited of 56 All 56 (JSON)