Quantifying discrepancies between probability distributions is a fundamental problem in statistics and machine learning, with applications to hypothesis testing, divergence estimation, and generative modeling.

In this talk, we introduce a framework for approximating f-divergences using rank statistics, without requiring density estimation or density-ratio estimation. Our approach relies on rank histograms that capture discrepancies between distributions, leading to simple, bounded, and statistically consistent estimators.

We discuss the theoretical properties of these approximations, including their lower-bound interpretation and convergence guarantees. We also extend the framework to high-dimensional settings through random projections, yielding sliced f-divergence estimators.

Finally, we present numerical experiments illustrating the effectiveness of the proposed methods for divergence estimation and training implicit generative models.

Based on: Approximating f-Divergences with Rank Statistics, Viktor Stein and José Manuel de Frutos (ICML 2026).