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Towards Diverse and Comprehensive Benchmarks for Mutual Information Estimation

arXiv 2607.03487 ↗First posted 3 Jul 2026cs.LG cs.AI cs.ITcited by 0

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Abstract (arXiv)

Mutual information (MI) estimation is a central problem in machine learning and statistics; however, existing benchmarks typically evaluate estimators on simplified, low-dimensional distributions, leaving their performance on complex, realistic data largely unexplored. We address this gap with a comprehensive benchmarking framework grounded in a unified copula-theoretic perspective that subsumes existing benchmarks as special cases. Within this framework, we propose two complementary families of tests: a copula-first family that systematically varies ground-truth MI, dimensionality, and marginal complexity using synthetic and flow-based transformations; and a marginals-first family that couples real-world image data with controlled dependency structures, extending the classic same-class-pairing paradigm. We use this suite to extensively evaluate three classes of estimators: non-parametric, discriminative, and generative. Contrary to prevailing assumptions, our results indicate that there is no universal winner: each category can systematically outperform all other estimators under specific setups. By analyzing these cases, we identify fundamental estimation barriers and propose new tests that more effectively stress these specific limitations. We share the open source code at https://github.com/VanessB/mutinfo.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 31 of its 52 references that are in the map. First posted on arXiv 3 Jul 2026.

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References · 31

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2018Representation Learning with Contrastive Predictive Codingcited by 7,662
  4. 2022Flow Matching for Generative Modelingcited by 5,426
  5. 2018Neural Ordinary Differential Equationscited by 3,733
  6. 2018Learning deep representations by mutual information estimation and maximizationcited by 1,265
  7. 2016InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Netscited by 858
  8. 2018MINE: Mutual Information Neural Estimationcited by 680
  9. 2019On Variational Bounds of Mutual Informationcited by 550
  10. 2019On Mutual Information Maximization for Representation Learningcited by 315
  11. 2018Formal Limitations on the Measurement of Mutual Informationcited by 189
  12. 2019Understanding the Limitations of Variational Mutual Information Estimatorscited by 140
19 more
  1. 2020Telescoping Density-Ratio Estimationcited by 108
  2. 2020Generalized Energy Based Modelscited by 73
  3. 2017Conditional independence testing based on a nearest-neighbor estimator of conditional mutual informationcited by 70
  4. 2021Density Ratio Estimation via Infinitesimal Classificationcited by 59
  5. 2023Beyond Normal: On the Evaluation of Mutual Information Estimatorscited by 37
  6. 2017Estimating Mutual Information for Discrete-Continuous Mixturescited by 34
  7. 2023MINDE: Mutual Information Neural Diffusion Estimationcited by 31
  8. 2016Efficient multivariate entropy estimation via k-nearest neighbour distancescited by 26
  9. 2024Mutual Information Estimation via Normalizing Flowscited by 22
  10. 2024Approximating mutual information of high-dimensional variables using learned representationscited by 21
  11. 2023Information Bottleneck Analysis of Deep Neural Networks via Lossy Compressioncited by 19
  12. 2023Mutual Information Estimation via f-Divergence and Data Derangementscited by 17
  13. 2022Diffeomorphic Information Neural Estimationcited by 10
  14. 2024A Benchmark Suite for Evaluating Neural Mutual Information Estimators on Unstructured Datasetscited by 10
  15. 2024Information Theoretic Text-to-Image Alignmentcited by 8
  16. 2023On the Properties and Estimation of Pointwise Mutual Information Profilescited by 7
  17. 2024Latent Abstractions in Generative Diffusion Modelscited by 4
  18. 2025Neural Mutual Information Estimation with Vector Copulascited by 4
  19. 2025A Neural Difference-of-Entropies Estimator for Mutual Informationcited by 1

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