mlsanityData to 14 Oct 2026

Multi-View Causal Representation Learning with Partial Observability

arXiv 2311.04056 ↗First posted 7 Nov 2023cs.LG cs.AIcited by 74

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Abstract (arXiv)

We present a unified framework for studying the identifiability of representations learned from simultaneously observed views, such as different data modalities. We allow a partially observed setting in which each view constitutes a nonlinear mixture of a subset of underlying latent variables, which can be causally related. We prove that the information shared across all subsets of any number of views can be learned up to a smooth bijection using contrastive learning and a single encoder per view. We also provide graphical criteria indicating which latent variables can be identified through a simple set of rules, which we refer to as identifiability algebra. Our general framework and theoretical results unify and extend several previous works on multi-view nonlinear ICA, disentanglement, and causal representation learning. We experimentally validate our claims on numerical, image, and multi-modal data sets. Further, we demonstrate that the performance of prior methods is recovered in different special cases of our setup. Overall, we find that access to multiple partial views enables us to identify a more fine-grained representation, under the generally milder assumption of partial observability.

Key facts. Cited by 74 papers in the map (data through 14 Oct 2026). Builds on 47 of its 82 references that are in the map. First posted on arXiv 7 Nov 2023.

Builds on

47 of 82 references.

References · 47

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2020A Simple Framework for Contrastive Learning of Visual Representationscited by 12,049
  3. 2023DINOv2: Learning Robust Visual Features without Supervisioncited by 7,974
  4. 2018Representation Learning with Contrastive Predictive Codingcited by 7,777
  5. 2021Emerging Properties in Self-Supervised Vision Transformerscited by 6,968
  6. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,739
  7. 2021Barlow Twins: Self-Supervised Learning via Redundancy Reductioncited by 1,838
  8. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 941
  9. 2020What Makes for Good Views for Contrastive Learning?cited by 846
  10. 2015Empirical Evaluation of Rectified Activations in Convolutional Networkcited by 519
  11. 2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 312
  12. 2018Towards a Definition of Disentangled Representationscited by 296
35 more
  1. 2018Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learningcited by 282
  2. 2020Weakly-Supervised Disentanglement Without Compromisescited by 239
  3. 2021Contrastive Learning Inverts the Data Generating Processcited by 221
  4. 2022Bridging the Gap to Real-World Object-Centric Learningcited by 220
  5. 2021Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICAcited by 160
  6. 2020Contrastive learning, multi-view redundancy, and linear modelscited by 146
  7. 2022Interventional Causal Representation Learningcited by 142
  8. 2022Weakly supervised causal representation learningcited by 140
  9. 2022CITRIS: Causal Identifiability from Temporal Intervened Sequencescited by 133
  10. 2020Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Codingcited by 122
  11. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 106
  12. 2020ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICAcited by 102
  13. 2019On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Datasetcited by 100
  14. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  15. 2019The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICAcited by 86
  16. 2022On the Identifiability of Nonlinear ICA: Sparsity and Beyondcited by 85
  17. 2022Linear Causal Disentanglement via Interventionscited by 84
  18. 2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
  19. 2018Learning Representations for Neural Network-Based Classification Using the Information Bottleneck Principlecited by 70
  20. 2022Identifiability of deep generative models without auxiliary informationcited by 70
  21. 2022Weakly Supervised Representation Learning with Sparse Perturbationscited by 65
  22. 2023Identifiability Results for Multimodal Contrastive Learningcited by 61
  23. 2023Causal Component Analysiscited by 56
  24. 2021Learning latent causal graphs via mixture oraclescited by 55
  25. 2023Score-based Causal Representation Learning with Interventionscited by 49
  26. 2022Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learningcited by 44
  27. 2021Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspectivecited by 37
  28. 2022Identifying Weight-Variant Latent Causal Modelscited by 34
  29. 2017Deep Generalized Canonical Correlation Analysiscited by 33
  30. 2023Leveraging sparse and shared feature activations for disentangled representation learningcited by 32
  31. 2023Causal Representation Learning Made Identifiable by Grouping of Observational Variablescited by 32
  32. 2022Causal Inference Through the Structural Causal Marginal Problemcited by 23
  33. 2021I Don't Need u: Identifiable Non-Linear ICA Without Side Informationcited by 21
  34. 2021Obtaining Causal Information by Merging Datasets with MAXENTcited by 9
  35. 2022Multi-View Independent Component Analysis with Shared and Individual Sourcescited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 18; 2025: 28; 2026: 28.

74 papers.

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  1. 2024A Sparsity Principle for Partially Observable Causal Representation Learningcited by 35
  2. 2024Unifying Causal Representation Learning with the Invariance Principlecited by 31
  3. 2024Marrying Causal Representation Learning with Dynamical Systems for Sciencecited by 23
  4. 2024Interaction Asymmetry: A General Principle for Learning Composable Abstractionscited by 20
  5. 2024On the Identification of Temporally Causal Representation with Instantaneous Dependencecited by 16
  6. 2024Linear Causal Representation Learning from Unknown Multi-node Interventionscited by 14
  7. 2025SmartCLIP: Modular Vision-language Alignment with Identification Guaranteescited by 14
  8. 2024Causal Representation Learning from Multimodal Biomedical Observationscited by 13
  9. 2025Towards Interpretable Deep Generative Models via Causal Representation Learningcited by 13
  10. 2024Smoke and Mirrors in Causal Downstream Taskscited by 12
  11. 2024Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environmentcited by 12
  12. 2024Beyond DAGs: A Latent Partial Causal Model for Multimodal Learningcited by 10
38 more
  1. 2025On the Value of Cross-Modal Misalignment in Multimodal Representation Learningcited by 10
  2. 2024Identifiable Object-Centric Representation Learning via Probabilistic Slot Attentioncited by 9
  3. 2024Language Agents Meet Causality -- Bridging LLMs and Causal World Modelscited by 9
  4. 2024Disentangling representations of retinal images with generative modelscited by 8
  5. 2024Identifiability Guarantees for Causal Disentanglement from Purely Observational Datacited by 7
  6. 2025Learning General Causal Structures with Hidden Dynamic Process for Climate Analysiscited by 7
  7. 2025What is causal about causal models and representations?cited by 6
  8. 2025Sample-efficient Learning of Concepts with Theoretical Guarantees: from Data to Concepts without Interventionscited by 6
  9. 2025Debiasing Reward Models by Representation Learning with Guaranteescited by 6
  10. 2024Towards the Causal Complete Cause of Multi-Modal Representation Learningcited by 5
  11. 2025Sanity Checking Causal Representation Learning on a Simple Real-World Systemcited by 5
  12. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 5
  13. 2024From Orthogonality to Dependency: Learning Disentangled Representation for Multi-Modal Time-Series Sensing Signalscited by 4
  14. 2025The Third Pillar of Causal Analysis? A Measurement Perspective on Causal Representationscited by 4
  15. 2025CausalVerse: Benchmarking Causal Representation Learning with Configurable High-Fidelity Simulationscited by 4
  16. 2026Structural Causal Bottleneck Modelscited by 4
  17. 2024OmniPrism: Learning Disentangled Visual Concept for Image Generationcited by 3
  18. 2025Disentangling Long-Short Term State Under Unknown Interventions for Online Time Series Forecastingcited by 3
  19. 2025Contextures: Representations from Contextscited by 3
  20. 2025Mechanistic Independence: A Principle for Identifiable Disentangled Representationscited by 3
  21. 2026Disentangling Dynamical Systems: Causal Representation Learning Meets Local Sparse Attentioncited by 3
  22. 2025Online Time Series Forecasting with Theoretical Guaranteescited by 2
  23. 2025Understanding Hardness of Vision-Language Compositionality from A Token-level Causal Lenscited by 2
  24. 2026The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergencecited by 2
  25. 2026A General Representation-Based Approach to Multi-Source Domain Adaptationcited by 2
  26. 2024Unsupervised discovery of the shared and private geometry in multi-view datacited by 1
  27. 2025Time Series Domain Adaptation via Latent Invariant Causal Mechanismcited by 1
  28. 2025On the Identifiability of Causal Abstractionscited by 1
  29. 2025Causal View of Time Series Imputation: Some Identification Results on Missing Mechanismcited by 1
  30. 2025Causal Representation Learning with Observational Grouping for CXR Classificationcited by 1
  31. 2025Intervening to Learn and Compose Causally Disentangled Representationscited by 1
  32. 2025Towards Causal Representation Learning with Observable Sources as Auxiliariescited by 1
  33. 2025Understanding Catastrophic Interference: On the Identifibility of Latent Representationscited by 1
  34. 2025Provable Affine Identifiability of Nonlinear CCA under Latent Distributional Priorscited by 1
  35. 2026Self-Supervised Learning from Structural Invariancecited by 1
  36. 2026Hierarchical Action Learning for Weakly-Supervised Action Segmentationcited by 1
  37. 2026Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixingcited by 1
  38. 2026Concept Modulation Models: A Unified Framework for Identifiability and Extrapolationcited by 1

50 most cited of 74 All 74 (JSON)