mlsanityData to 14 Oct 2026

Generalizing Nonlinear ICA Beyond Structural Sparsity

arXiv 2311.00866 ↗First posted 1 Nov 2023cs.LG eess.SP stat.MLcited by 34

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Abstract (arXiv)

Nonlinear independent component analysis (ICA) aims to uncover the true latent sources from their observable nonlinear mixtures. Despite its significance, the identifiability of nonlinear ICA is known to be impossible without additional assumptions. Recent advances have proposed conditions on the connective structure from sources to observed variables, known as Structural Sparsity, to achieve identifiability in an unsupervised manner. However, the sparsity constraint may not hold universally for all sources in practice. Furthermore, the assumptions of bijectivity of the mixing process and independence among all sources, which arise from the setting of ICA, may also be violated in many real-world scenarios. To address these limitations and generalize nonlinear ICA, we propose a set of new identifiability results in the general settings of undercompleteness, partial sparsity and source dependence, and flexible grouping structures. Specifically, we prove identifiability when there are more observed variables than sources (undercomplete), and when certain sparsity and/or source independence assumptions are not met for some changing sources. Moreover, we show that even in cases with flexible grouping structures (e.g., part of the sources can be divided into irreducible independent groups with various sizes), appropriate identifiability results can also be established. Theoretical claims are supported empirically on both synthetic and real-world datasets.

Key facts. Cited by 34 papers in the map (data through 14 Oct 2026). Builds on 22 of its 44 references that are in the map. First posted on arXiv 1 Nov 2023.

Builds on

22 of 44 references.

References · 22

  1. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  2. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 941
  3. 2019Variational Autoencoders and Nonlinear ICA: A Unifying Frameworkcited by 503
  4. 2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 312
  5. 2018Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learningcited by 282
  6. 2016Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICAcited by 273
  7. 2017Variational Inference of Disentangled Latent Concepts from Unlabeled Observationscited by 241
  8. 2021Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICAcited by 160
  9. 2020ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICAcited by 102
  10. 2021Learning Temporally Causal Latent Processes from General Temporal Datacited by 98
  11. 2020Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)cited by 92
  12. 2022On the Identifiability of Nonlinear ICA: Sparsity and Beyondcited by 85
10 more
  1. 2020Measuring Disentanglement: A Review of Metricscited by 70
  2. 2022Identifiability of deep generative models without auxiliary informationcited by 70
  3. 2021Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICAcited by 64
  4. 2022Temporally Disentangled Representation Learningcited by 61
  5. 2022Function Classes for Identifiable Nonlinear Independent Component Analysiscited by 53
  6. 2018Learning Latent Subspaces in Variational Autoencoderscited by 51
  7. 2019Unsupervised Model Selection for Variational Disentangled Representation Learningcited by 46
  8. 2022Partial Disentanglement via Mechanism Sparsitycited by 29
  9. 2021Multi-Facet Clustering Variational Autoencoderscited by 28
  10. 2014Support recovery without incoherence: A case for nonconvex regularizationcited by 25

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 8; 2025: 14; 2026: 12.

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  1. 2024Causal Representation Learning from Multiple Distributions: A General Settingcited by 68
  2. 2024A Sparsity Principle for Partially Observable Causal Representation Learningcited by 35
  3. 2025Thought Communication in Multiagent Collaborationcited by 30
  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. 2025From superposition to sparse codes: interpretable representations in neural networkscited by 16
  7. 2024Causal Temporal Representation Learning with Nonstationary Sparse Transitioncited by 13
  8. 2024Causal Representation Learning from Multimodal Biomedical Observationscited by 13
  9. 2025Towards Interpretable Deep Generative Models via Causal Representation Learningcited by 13
  10. 2025Towards Identifiability of Hierarchical Temporal Causal Representation Learningcited by 9
  11. 2025Learning General Causal Structures with Hidden Dynamic Process for Climate Analysiscited by 7
  12. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 5
22 more
  1. 2025Synergy Between Sufficient Changes and Sparse Mixing Procedure for Disentangled Representation Learningcited by 4
  2. 2025Nonparametric Factor Analysis and Beyondcited by 4
  3. 2025Diverse Influence Component Analysis: A Geometric Approach to Nonlinear Mixture Identifiabilitycited by 4
  4. 2025Mechanistic Independence: A Principle for Identifiable Disentangled Representationscited by 3
  5. 2025Nonparametric Identification of Latent Conceptscited by 3
  6. 2025Online Time Series Forecasting with Theoretical Guaranteescited by 2
  7. 2026Content-Style Identification via Differential Independencecited by 2
  8. 2025Towards Causal Representation Learning with Observable Sources as Auxiliariescited by 1
  9. 2025Understanding Catastrophic Interference: On the Identifibility of Latent Representationscited by 1
  10. 2026Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixingcited by 1
  11. 2026MOSAIC: Module Discovery via Sparse Additive Identifiable Causal Learning for Scientific Time Seriescited by 1
  12. 2024Identifiability of a statistical model with two latent vectors: Importance of the dimensionality relation and application to graph embeddingcited by 0
  13. 2024Continual Learning of Nonlinear Independent Representationscited by 0
  14. 2025Position: Beyond Sensitive Attributes, ML Fairness Should Quantify Structural Injustice via Social Determinantscited by 0
  15. 2026Domain Transfer Becomes Identifiable via a Single Alignmentcited by 0
  16. 2026Identifiable Multimodal Causal Representation Learning under Partial Latent Sharingcited by 0
  17. 2026MoVA: Learning Asymmetric Dual Projections for Modular Long Video-Text Alignmentcited by 0
  18. 2026Beyond ICA: Identifiability by Symmetry Breakingcited by 0
  19. 2026Kinks vs. Smoothness: Identifiability of Real Analytic nICA for Laplace-like Sourcescited by 0
  20. 2026Identification of Nonlinear and Dependent Latent Factor Structure through Clique Searchcited by 0
  21. 2026Towards Identifiable Representations under Misspecified Structurecited by 0
  22. 2026Variance Fingerprints: Component-Wise Identification of Content Factors by Augmentation Designcited by 0