mlsanityData to 7 Oct 2026

The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA

arXiv 1905.06642 ↗First posted 16 May 2019stat.ML cs.LGcited by 86

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Abstract (arXiv)

We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available.

Key facts. Cited by 86 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 May 2019.

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Citing papers per year: 2021: 11; 2022: 10; 2023: 18; 2024: 17; 2025: 20; 2026: 10.

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  9. 2023Identifiability Results for Multimodal Contrastive Learningcited by 58
  10. 2025Projecting Assumptions: The Duality Between Sparse Autoencoders and Concept Geometrycited by 58
  11. 2023Causal Component Analysiscited by 56
  12. 2022Mechanistic Mode Connectivitycited by 50
38 more
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  5. 2024InfoNCE: Identifying the Gap Between Theory and Practicecited by 39
  6. 2021Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspectivecited by 37
  7. 2021On the Limitations of Multimodal VAEscited by 37
  8. 2021Contrastively Disentangled Sequential Variational Autoencodercited by 34
  9. 2022Indeterminacy in Generative Models: Characterization and Strong Identifiabilitycited by 33
  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. 2024Cross-Entropy Is All You Need To Invert the Data Generating Processcited by 30
  13. 2022Embrace the Gap: VAEs Perform Independent Mechanism Analysiscited by 28
  14. 2023Multi-Domain Causal Representation Learning via Weak Distributional Invariancescited by 23
  15. 2021I Don't Need u: Identifiable Non-Linear ICA Without Side Informationcited by 21
  16. 2023From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modelingcited by 21
  17. 2023Self-Supervised Disentanglement by Leveraging Structure in Data Augmentationscited by 16
  18. 2024Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learningcited by 16
  19. 2024On the Identification of Temporally Causal Representation with Instantaneous Dependencecited by 15
  20. 2023Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelcited by 14
  21. 2024All or None: Identifiable Linear Properties of Next-token Predictors in Language Modelingcited by 14
  22. 2025SmartCLIP: Modular Vision-language Alignment with Identification Guaranteescited by 14
  23. 2023Towards a Unified Framework of Contrastive Learning for Disentangled Representationscited by 13
  24. 2024Counterfactual Generation with Identifiability Guaranteescited by 13
  25. 2025Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lenscited by 13
  26. 2024Causal Representation Learning from Multimodal Biomedical Observationscited by 12
  27. 2022Provable concept learning for interpretable predictions using variational autoencoderscited by 9
  28. 2023An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysiscited by 9
  29. 2024Beyond DAGs: A Latent Partial Causal Model for Multimodal Learningcited by 9
  30. 2026Cross-Modal Redundancy and the Geometry of Vision-Language Embeddingscited by 9
  31. 2021Identifiability-Guaranteed Simplex-Structured Post-Nonlinear Mixture Learning via Autoencodercited by 7
  32. 2022On Finite-Sample Identifiability of Contrastive Learning-Based Nonlinear Independent Component Analysiscited by 7
  33. 2023Independent Mechanism Analysis and the Manifold Hypothesiscited by 7
  34. 2022Multi-View Independent Component Analysis with Shared and Individual Sourcescited by 6
  35. 2024Propensity Score Alignment of Unpaired Multimodal Datacited by 6
  36. 2022Probing the Robustness of Independent Mechanism Analysis for Representation Learningcited by 5
  37. 2023Latent Processes Identification From Multi-View Time Seriescited by 5
  38. 2024Causal Representation Learning in Temporal Data via Single-Parent Decodingcited by 5

50 most cited of 86 All 86 (JSON)