Speaker: José Manuel de Frutos Porras.
Abstract: Comparing probability distributions from samples is a fundamental problem in statistics and machine learning, particularly when working with implicit generative models whose densities cannot be evaluated. In this talk, I will present an approach to approximating f-divergences through rank statistics, without explicitly estimating densities or density ratios. The construction compares a rank distribution with the uniform distribution using a discrete f-divergence. At the population level, these approximations provide lower bounds on the target divergence and converge monotonically as the rank resolution increases. I will discuss convergence rates and statistical guarantees for sample-based estimators, as well as an extension to multivariate distributions through random projections. Finally, I will illustrate the approach with divergence estimation experiments and applications to generative modelling. This is joint work with Viktor Stein.
Paper: https://arxiv.org/abs/2601.22784