mlsanityData to 14 Oct 2026

LIDL: Local Intrinsic Dimension Estimation Using Approximate Likelihood

arXiv 2206.14882 ↗First posted 29 Jun 2022stat.ML cs.LGcited by 30

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Abstract (arXiv)

Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of dimensionality. We attempt to address that challenge by proposing a novel approach to the problem: Local Intrinsic Dimension estimation using approximate Likelihood (LIDL). Our method relies on an arbitrary density estimation method as its subroutine and hence tries to sidestep the dimensionality challenge by making use of the recent progress in parametric neural methods for likelihood estimation. We carefully investigate the empirical properties of the proposed method, compare them with our theoretical predictions, and show that LIDL yields competitive results on the standard benchmarks for this problem and that it scales to thousands of dimensions. What is more, we anticipate this approach to improve further with the continuing advances in the density estimation literature.

Key facts. Cited by 30 papers in the map (data through 14 Oct 2026). Builds on 20 of its 45 references that are in the map. First posted on arXiv 29 Jun 2022.

Builds on

20 of 45 references.

References · 20

  1. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  2. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  3. 2015Variational Inference with Normalizing Flowscited by 2,170
  4. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  5. 2014NICE: Non-linear Independent Components Estimationcited by 1,058
  6. 2017Masked Autoregressive Flow for Density Estimationcited by 684
  7. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 672
  8. 2019Neural Spline Flowscited by 596
  9. 2017Wasserstein Auto-Encoderscited by 373
  10. 2018Measuring the Intrinsic Dimension of Objective Landscapescited by 370
  11. 2021The Intrinsic Dimension of Images and Its Impact on Learningcited by 315
  12. 2019Intrinsic dimension of data representations in deep neural networkscited by 282
8 more
  1. 2018Estimating the intrinsic dimension of datasets by a minimal neighborhood informationcited by 250
  2. 2020Flows for simultaneous manifold learning and density estimationcited by 118
  3. 2021Scikit-dimension: a Python package for intrinsic dimension estimationcited by 68
  4. 2021Rectangular Flows for Manifold Learningcited by 50
  5. 2021Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flowscited by 31
  6. 2018On the Latent Space of Wasserstein Auto-Encoderscited by 22
  7. 2019Estimating the effective dimension of large biological datasets using Fisher separability analysiscited by 19
  8. 2018Unsupervised representation learning using convolutional and stacked auto-encoders: a domain and cross-domain feature space analysiscited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 4; 2023: 3; 2024: 8; 2025: 7; 2026: 8.

30 papers.

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  1. 2022Verifying the Union of Manifolds Hypothesis for Image Datacited by 64
  2. 2024A Geometric View of Data Complexity: Efficient Local Intrinsic Dimension Estimation with Diffusion Modelscited by 42
  3. 2024A Geometric Framework for Understanding Memorization in Generative Modelscited by 40
  4. 2024On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion modelscited by 23
  5. 2024Diffusion Models as Cartoonists: The Curious Case of High Density Regionscited by 21
  6. 2024Understanding and Mitigating Memorization in Generative Models via Sharpness of Probability Landscapescited by 21
  7. 2025Learning normalized image densities via dual score matchingcited by 18
  8. 2022Relating Regularization and Generalization through the Intrinsic Dimension of Activationscited by 9
  9. 2022Denoising Deep Generative Modelscited by 6
  10. 2025LeapFactual: Reliable Visual Counterfactual Explanation Using Conditional Flow Matchingcited by 5
  11. 2023One-Line-of-Code Data Mollification Improves Optimization of Likelihood-based Generative Modelscited by 4
  12. 2023Adversarial Estimation of Topological Dimension with Harmonic Score Mapscited by 4
18 more
  1. 2025A Connection Between Score Matching and Local Intrinsic Dimensioncited by 4
  2. 2022Impact of dataset size and long-term ECoG-based BCI usage on deep learning decoders performancecited by 3
  3. 2024Score-based Pullback Riemannian Geometry: Extracting the Data Manifold Geometry using Anisotropic Flowscited by 3
  4. 2025On Convolutions, Intrinsic Dimension, and Diffusion Modelscited by 3
  5. 2026IdEst: Assessing Self-Supervised Learning Representations via Intrinsic Dimensioncited by 2
  6. 2023A survey of manifold learning and its applications for multimediacited by 1
  7. 2024Dimensionality-Aware Outlier Detection: Theoretical and Experimental Analysiscited by 1
  8. 2024A Wiener Process Perspective on Local Intrinsic Dimension Estimation Methodscited by 1
  9. 2025Geometry-Guided Adversarial Prompt Detection via Curvature and Local Intrinsic Dimensioncited by 1
  10. 2025Estimating Dataset Dimension via Singular Metrics under the Manifold Hypothesis: Application to Inverse Problemscited by 1
  11. 2026A Universal Nearest-Neighbor Estimator for Intrinsic Dimensionalitycited by 1
  12. 2026Local Intrinsic Dimension Unveils Hallucinations in Diffusion Modelscited by 1
  13. 2026SoftSAE: Dynamic Top-K Selection for Adaptive Sparse Autoencoderscited by 1
  14. 2026Style-CCL: Content-Preserving Style Transfer via Curriculum Continual Learningcited by 1
  15. 2025HomID : Benchmarking Intrinsic Dimension Estimators on Homogenous Manifolds with Anisotropic Embeddingscited by 0
  16. 2026On the Use of Bagging for Local Intrinsic Dimensionality Estimationcited by 0
  17. 2026One Inverse Step is a Convex Program: Bayes-Limit Calibration of Diffusion Inversioncited by 0
  18. 2026Minimax Lower Bound for Estimating Diffusion-based Local Intrinsic Dimensioncited by 0