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Approximating f-Divergences with Rank Statistics

arXiv 2601.22784 ↗First posted 30 Jan 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

We introduce a rank-statistic approximation of f-divergences that avoids explicit density-ratio estimation by working directly with the distribution of ranks. For a resolution parameter K, we map the mismatch between two univariate distributions μ and nu to a rank histogram on 0, ldots, K and measure its deviation from uniformity via a discrete f-divergence, yielding a rank-statistic divergence estimator. We prove that the resulting estimator of the divergence is monotone in K, is always a lower bound of the true f-divergence, and we establish quantitative convergence rates for K→∞ under mild regularity of the quantile-domain density ratio. To handle high-dimensional data, we define the sliced rank-statistic f-divergence by averaging the univariate construction over random projections, and we provide convergence results for the sliced limit as well. We also derive finite-sample deviation bounds along with asymptotic normality results for the estimator. Finally, we empirically validate the approach by benchmarking against neural baselines and illustrating its use as a learning objective in generative modeling experiments.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 26 of its 60 references that are in the map. First posted on arXiv 30 Jan 2026.

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References · 26

  1. 2019Benchmarking Neural Network Robustness to Common Corruptions and Perturbationscited by 2,857
  2. 2017Improved Training of Wasserstein GANscited by 2,223
  3. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  4. 2018MINE: Mutual Information Neural Estimationcited by 680
  5. 2018Assessing Generative Models via Precision and Recallcited by 401
  6. 2016Revisiting Classifier Two-Sample Testscited by 258
  7. 2019Generalized Sliced Wasserstein Distancescited by 205
  8. 2019Max-Sliced Wasserstein Distance and its use for GANscited by 118
  9. 2020Mitigating Bias in Calibration Error Estimationcited by 100
  10. 2019Subspace Robust Wasserstein Distancescited by 89
  11. 2020Statistical and Topological Properties of Sliced Probability Divergencescited by 83
  12. 2018Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusionscited by 77
14 more
  1. 2019Sliced Wasserstein Generative Modelscited by 61
  2. 2016Generative Multi-Adversarial Networkscited by 60
  3. 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
  4. 2019Practical and Consistent Estimation of f-Divergencescited by 24
  5. 2021Non-Asymptotic Performance Guarantees for Neural Estimation of mathsff-Divergencescited by 15
  6. 2024Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spacescited by 15
  7. 2021MCL-GAN: Generative Adversarial Networks with Multiple Specialized Discriminatorscited by 11
  8. 2019Revisiting Precision and Recall Definition for Generative Model Evaluationcited by 9
  9. 2023Precision-Recall Divergence Optimization for Generative Modeling with GANs and Normalizing Flowscited by 9
  10. 2014Multivariate f-Divergence Estimation With Confidencecited by 7
  11. 2020On the Theoretical Equivalence of Several Trade-Off Curves Assessing Statistical Proximitycited by 6
  12. 2024Training Implicit Generative Models via an Invariant Statistical Losscited by 3
  13. 2024Robust training of implicit generative models for multivariate and heavy-tailed distributions with an invariant statistical losscited by 2
  14. 2025Explicit Density Approximation for Neural Implicit Samplers Using a Bernstein-Based Convex Divergencecited by 1

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