Data to 7 Oct 2026

Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning

arXiv 1805.08651 ↗First posted 22 May 2018stat.ML cs.LGcited by 278

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Abstract (arXiv)

Nonlinear ICA is a fundamental problem for unsupervised representation learning, emphasizing the capacity to recover the underlying latent variables generating the data (i.e., identifiability). Recently, the very first identifiability proofs for nonlinear ICA have been proposed, leveraging the temporal structure of the independent components. Here, we propose a general framework for nonlinear ICA, which, as a special case, can make use of temporal structure. It is based on augmenting the data by an auxiliary variable, such as the time index, the history of the time series, or any other available information. We propose to learn nonlinear ICA by discriminating between true augmented data, or data in which the auxiliary variable has been randomized. This enables the framework to be implemented algorithmically through logistic regression, possibly in a neural network. We provide a comprehensive proof of the identifiability of the model as well as the consistency of our estimation method. The approach not only provides a general theoretical framework combining and generalizing previously proposed nonlinear ICA models and algorithms, but also brings practical advantages.

Key facts. Cited by 278 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 May 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 24; 2022: 43; 2023: 56; 2024: 45; 2025: 54; 2026: 56.

278 papers.

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2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 308
2021Contrastive Learning Inverts the Data Generating Processcited by 220
2021Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICAcited by 158
2022Interventional Causal Representation Learningcited by 140
2022CITRIS: Causal Identifiability from Temporal Intervened Sequencescited by 132
2022Learnable latent embeddings for joint behavioral and neural analysiscited by 113
2022Disentangled Representation Learningcited by 111
2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
2021Independent mechanism analysis, a new concept?cited by 96
2021Learning Temporally Causal Latent Processes from General Temporal Datacited by 96
2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
2022On the Identifiability of Nonlinear ICA: Sparsity and Beyondcited by 84

38 more

2022Linear Causal Disentanglement via Interventionscited by 84
2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
2023Multi-View Causal Representation Learning with Partial Observabilitycited by 72
2021Unsupervised Learning of Compositional Energy Conceptscited by 71
2022Identifiability of deep generative models without auxiliary informationcited by 70
2024Causal Representation Learning from Multiple Distributions: A General Settingcited by 67
2021Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICAcited by 64
2022Weakly Supervised Representation Learning with Sparse Perturbationscited by 64
2021Visual Representation Learning Does Not Generalize Strongly Within the Same Domaincited by 60
2022Temporally Disentangled Representation Learningcited by 59
2023Concept Algebra for (Score-Based) Text-Controlled Generative Modelscited by 59
2022ZIN: When and How to Learn Invariance Without Environment Partition?cited by 58
2023Identifiability of latent-variable and structural-equation models: from linear to nonlinearcited by 58
2023Identifiability Results for Multimodal Contrastive Learningcited by 58
2023Causal Component Analysiscited by 56
2023Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolationcited by 56
2022Mixing Up Contrastive Learning: Self-Supervised Representation Learning for Time Seriescited by 54
2022Function Classes for Identifiable Nonlinear Independent Component Analysiscited by 53
2023High Fidelity Image Counterfactuals with Probabilistic Causal Modelscited by 53
2022Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systemscited by 50
2023Score-based Causal Representation Learning with Interventionscited by 49
2022CLEAR: Generative Counterfactual Explanations on Graphscited by 48
2023Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learningcited by 48
2023Provably Learning Object-Centric Representationscited by 45
2022Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learningcited by 44
2021Nonlinear Invariant Risk Minimization: A Causal Approachcited by 42
2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
2023Provable Compositional Generalization for Object-Centric Learningcited by 41
2022From Statistical to Causal Learningcited by 40
2023Understanding Masked Autoencoders via Hierarchical Latent Variable Modelscited by 39
2023BISCUIT: Causal Representation Learning from Binary Interactionscited by 38
2021Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspectivecited by 37
2023Subspace Identification for Multi-Source Domain Adaptationcited by 36
2023General Identifiability and Achievability for Causal Representation Learningcited by 34
2024A Sparsity Principle for Partially Observable Causal Representation Learningcited by 34
2022Indeterminacy in Generative Models: Characterization and Strong Identifiabilitycited by 33
2022Identifying Weight-Variant Latent Causal Modelscited by 33
2023Generalizing Nonlinear ICA Beyond Structural Sparsitycited by 33

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