mlsanityData to 7 Oct 2026

Intrinsic Dimension Estimation Using Wasserstein Distances

arXiv 2106.04018 ↗First posted 8 Jun 2021stat.ML cs.LGcited by 20

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Abstract (arXiv)

It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension of a given population distribution from a finite sample. We introduce a new estimator of the intrinsic dimension and provide finite sample, non-asymptotic guarantees. We then apply our techniques to get new sample complexity bounds for Generative Adversarial Networks (GANs) depending only on the intrinsic dimension of the data.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 9 of its 77 references that are in the map. First posted on arXiv 8 Jun 2021.

Builds on

9 of 77 references.

References · 9

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  2. 2019LOGAN: Latent Optimisation for Generative Adversarial Networkscited by 42
  3. 2020Statistical guarantees for generative models without dominationcited by 27
  4. 2019Nonparametric Density Estimation & Convergence Rates for GANs under Besov IPM Lossescited by 22
  5. 2013Adaptive Metric Dimensionality Reductioncited by 14
  6. 2020Fast Mixing of Multi-Scale Langevin Dynamics under the Manifold Hypothesiscited by 11
  7. 2016Minimax Rates for Estimating the Dimension of a Manifoldcited by 10
  8. 2020Functions with average smoothness: structure, algorithms, and learningcited by 6
  9. 2017Adaptive Nonparametric Clusteringcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 5; 2024: 6; 2025: 4; 2026: 3.

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  1. 2023Manifold learning: what, how, and whycited by 66
  2. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionalitycited by 44
  3. 2022Discovering Conservation Laws using Optimal Transport and Manifold Learningcited by 12
  4. 2023Sample Complexity Bounds for Estimating Probability Divergences under Invariancescited by 11
  5. 2022Relating Regularization and Generalization through the Intrinsic Dimension of Activationscited by 9
  6. 2023Data-Copying in Generative Models: A Formal Frameworkcited by 9
  7. 2023CA-PCA: Manifold Dimension Estimation, Adapted for Curvaturecited by 4
  8. 2025Deep Generative Models: Complexity, Dimensionality, and Approximationcited by 4
  9. 2024Scale adaptive and robust intrinsic dimension estimation via optimal neighbourhood identificationcited by 3
  10. 2024Generative adversarial learning with optimal input dimension and its adaptive generator architecturecited by 1
  11. 2024Blessing of Dimensionality for Approximating Sobolev Classes on Manifoldscited by 1
  12. 2024Geometric Collaborative Filtering with Convergencecited by 1
8 more
  1. 2026Rate-Optimal Noise Annealing in Semi-Dual Neural Optimal Transport: Tangential Identifiability, Off-Manifold Ambiguity, and Guaranteed Recoverycited by 1
  2. 2023Manifold Regularization for Memory-Efficient Training of Deep Neural Networkscited by 0
  3. 2024On consistent estimation of dimension valuescited by 0
  4. 2025A Survey and Comparative Evaluation of Intrinsic Dimension Estimators under the Manifold Hypothesiscited by 0
  5. 2025HomID : Benchmarking Intrinsic Dimension Estimators on Homogenous Manifolds with Anisotropic Embeddingscited by 0
  6. 2025Manifold Dimension Estimation via Local Graph Structurecited by 0
  7. 2026Geometry-Aware Optimal Transport: Fast Intrinsic Dimension and Wasserstein Distance Estimationcited by 0
  8. 2026A Unified Framework for In-Context Learning with Causal and Masked Language Modelscited by 0