mlsanityData to 14 Oct 2026

Independent mechanism analysis, a new concept?

arXiv 2106.05200 ↗First posted 9 Jun 2021stat.ML cs.AI cs.LGcited by 97

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Abstract (arXiv)

Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof. Unfortunately, when the mixing is nonlinear, the model is provably nonidentifiable, since statistical independence alone does not sufficiently constrain the problem. Identifiability can be recovered in settings where additional, typically observed variables are included in the generative process. We investigate an alternative path and consider instead including assumptions reflecting the principle of independent causal mechanisms exploited in the field of causality. Specifically, our approach is motivated by thinking of each source as independently influencing the mixing process. This gives rise to a framework which we term independent mechanism analysis. We provide theoretical and empirical evidence that our approach circumvents a number of nonidentifiability issues arising in nonlinear blind source separation.

Key facts. Cited by 97 papers in the map (data through 14 Oct 2026). Builds on 38 of its 131 references that are in the map. First posted on arXiv 9 Jun 2021.

Builds on

38 of 131 references.

References · 38

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  2. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  3. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 941
  4. 2015Causal inference using invariant prediction: identification and confidence intervalscited by 536
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  9. 2019Residual Flows for Invertible Generative Modelingcited by 257
  10. 2013Causal Discovery with Continuous Additive Noise Modelscited by 255
  11. 2019Recurrent Independent Mechanismscited by 219
  12. 2018Neural Autoregressive Flowscited by 208
26 more
  1. 2017Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributionscited by 126
  2. 2018Anchor regression: heterogeneous data meets causalitycited by 118
  3. 2017Learning Independent Causal Mechanismscited by 105
  4. 2020Causal Autoregressive Flowscited by 99
  5. 2020The Hessian Penalty: A Weak Prior for Unsupervised Disentanglementcited by 92
  6. 2019The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICAcited by 86
  7. 2018Woulda, Coulda, Shoulda: Counterfactually-Guided Policy Searchcited by 82
  8. 2020Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Seriescited by 77
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  11. 2019Causal Discovery with General Non-Linear Relationships Using Non-Linear ICAcited by 58
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  20. 2017Faster independent component analysis by preconditioning with Hessian approximationscited by 16
  21. 2020Relative gradient optimization of the Jacobian term in unsupervised deep learningcited by 16
  22. 2019Semi-Supervised Learning, Causality and the Conditional Cluster Assumptioncited by 15
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  26. 2014Justifying Information-Geometric Causal Inferencecited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 16; 2023: 29; 2024: 19; 2025: 16; 2026: 16.

97 papers.

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  1. 2022Weakly supervised causal representation learningcited by 140
  2. 2022CITRIS: Causal Identifiability from Temporal Intervened Sequencescited by 133
  3. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 106
  4. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  5. 2022On the Identifiability of Nonlinear ICA: Sparsity and Beyondcited by 85
  6. 2022Identifiability of deep generative models without auxiliary informationcited by 70
  7. 2023Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcutscited by 63
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  9. 2023Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolationcited by 58
  10. 2023Causal Component Analysiscited by 56
  11. 2022Function Classes for Identifiable Nonlinear Independent Component Analysiscited by 53
  12. 2022Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systemscited by 51
38 more
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  2. 2023Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learningcited by 48
  3. 2023Provably Learning Object-Centric Representationscited by 45
  4. 2022Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learningcited by 44
  5. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  6. 2023Provable Compositional Generalization for Object-Centric Learningcited by 41
  7. 2022From Statistical to Causal Learningcited by 40
  8. 2023Disentanglement via Latent Quantizationcited by 40
  9. 2023BISCUIT: Causal Representation Learning from Binary Interactionscited by 38
  10. 2024BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcutscited by 37
  11. 2024Emergence of Hidden Capabilities: Exploring Learning Dynamics in Concept Spacecited by 35
  12. 2022Indeterminacy in Generative Models: Characterization and Strong Identifiabilitycited by 33
  13. 2023Causal Representation Learning Made Identifiable by Grouping of Observational Variablescited by 32
  14. 2021Properties from Mechanisms: An Equivariance Perspective on Identifiable Representation Learningcited by 30
  15. 2024Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Modelscited by 29
  16. 2022Embrace the Gap: VAEs Perform Independent Mechanism Analysiscited by 28
  17. 2023From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modelingcited by 22
  18. 2023Object-centric architectures enable efficient causal representation learningcited by 21
  19. 2024Position: Understanding LLMs Requires More Than Statistical Generalizationcited by 21
  20. 2024Interaction Asymmetry: A General Principle for Learning Composable Abstractionscited by 20
  21. 2024A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcutscited by 19
  22. 2022Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitionscited by 18
  23. 2023Identifying Linearly-Mixed Causal Representations from Multi-Node Interventionscited by 18
  24. 2023Self-Supervised Disentanglement by Leveraging Structure in Data Augmentationscited by 17
  25. 2024Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learningcited by 16
  26. 2022When are Post-hoc Conceptual Explanations Identifiable?cited by 14
  27. 2023Learning Causally Disentangled Representations via the Principle of Independent Causal Mechanismscited by 14
  28. 2023A Review of Change of Variable Formulas for Generative Modelingcited by 13
  29. 2023Towards a Unified Framework of Contrastive Learning for Disentangled Representationscited by 13
  30. 2024Tripod: Three Complementary Inductive Biases for Disentangled Representation Learningcited by 13
  31. 2025Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lenscited by 13
  32. 2025Towards Interpretable Deep Generative Models via Causal Representation Learningcited by 13
  33. 2024Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environmentcited by 12
  34. 2024Counterfactual Generative Modeling with Variational Causal Inferencecited by 11
  35. 2023An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysiscited by 9
  36. 2025Position: An Empirically Grounded Identifiability Theory Will Accelerate Self-Supervised Learning Researchcited by 9
  37. 2026Causality is Key for Interpretability Claims to Generalisecited by 8
  38. 2023Independent Mechanism Analysis and the Manifold Hypothesiscited by 7

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