Approximating f-Divergences with Rank Statistics

Authors: Viktor Stein and José Manuel de Frutos
Venue: International Conference on Machine Learning (ICML), 2026
Links: arXiv · PDF · OpenReview · Code

Overview

We introduce rank-statistic approximations of f-divergences that can be estimated directly from samples, avoiding explicit density or density-ratio estimation. The method compares distributions through rank histograms and yields a family of increasingly fine approximations to the underlying f-divergence.

For high-dimensional distributions, the construction extends through random projections, leading to sliced rank-statistic f-divergences. The framework can be used for divergence estimation, two-sample comparison, and training implicit generative models with rank-based objectives.

Relevance to GANs and f-GANs

Many generative modeling methods compare a model distribution with the data distribution through statistical divergences. In particular, f-GANs connect adversarial generative modeling with f-divergence minimization. Our contribution is not a GAN training algorithm itself; rather, it provides a way to approximate f-divergences directly from samples without explicit density or density-ratio estimation.

This makes the method relevant to researchers working on GAN evaluation, f-GAN objectives, sample-based comparison of real and generated distributions, and density-ratio-free divergence estimation. In settings where only samples from the data distribution and generator are available, rank-statistic f-divergences provide a direct statistical comparison tool.

Topics

f-divergences · rank statistics · divergence estimation · density-ratio-free estimation · two-sample testing · sliced divergences · implicit generative models · generative adversarial networks (GANs) · f-GAN · generated sample evaluation · statistical machine learning

Abstract

The official abstract is available on arXiv. This page intentionally avoids duplicating a potentially stale version until the final conference version is published; the structured metadata above points search engines and scholarly indexers to the canonical arXiv record and PDF.

BibTeX

@inproceedings{stein2026approximating,
  title={Approximating f-Divergences with Rank Statistics},
  author={Stein, Viktor and de Frutos, Jos\'e Manuel},
  booktitle={Proceedings of the International Conference on Machine Learning},
  year={2026}
}

Recommended citation: Viktor Stein and José Manuel de Frutos. (2026). "Approximating f-Divergences with Rank Statistics." International Conference on Machine Learning (ICML).
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