José Manuel de Frutos Porras will defend his doctoral thesis, entitled “Rank-Based Divergences for Implicit Generative Modeling”, conducted under the supervision of Professor Joaquín Míguez Arenas and Professor Manuel Alberto Vázquez López.
The public defense will take place on Friday, November 13th, at 11:00 AM, in the Multimedia Room (3.S1.08), Rey Pastor Building, Leganés Campus, Universidad Carlos III de Madrid.
The thesis addresses fundamental challenges in implicit generative modelling, a powerful approach to learning complex probability distributions directly from samples, even when their probability densities cannot be explicitly evaluated. These models offer considerable flexibility but also present significant difficulties when it comes to training, evaluating and comparing distributions, particularly in high-dimensional settings or when dealing with heavy-tailed data. The research explores statistical methods based on comparison ranks as an alternative to conventional approaches that require explicit density evaluations.
A first major contribution of the dissertation is the introduction of the Invariant Statistical Loss (ISL), a novel statistical discrepancy that enables probability distributions to be compared using only samples. The work establishes its theoretical properties and investigates its application to generative modelling. Building on this framework, the thesis develops extensions to multivariate and heavy-tailed distributions, incorporating sliced formulations and techniques inspired by extreme value theory. These developments broaden the applicability of rank-based methods to more challenging statistical settings.
The second part of the thesis investigates a dual formulation of ISL, establishing important convexity properties and connections with Bernstein polynomial approximation. These theoretical results enable the explicit reconstruction of probability densities from implicit generative models, providing a bridge between sample-based learning and density estimation. This approach offers new possibilities for analysing and interpreting generative models whose underlying probability distributions are otherwise difficult to characterise.
Finally, the dissertation introduces rank-based approximations of f-divergences, a broad family of statistical measures used to quantify differences between probability distributions. The research establishes convergence results and statistical guarantees for these approximations and explores their applications to generative learning and particle transport, further extending the theoretical and computational tools available for distribution comparison and optimisation.
Overall, this dissertation advances the theoretical foundations of implicit generative modelling by developing a comprehensive framework for learning, comparing and reconstructing probability distributions without requiring explicit density evaluations. Its contributions provide new statistical insights and computational methods for addressing complex problems in modern generative modelling.
Everyone is warmly invited to attend the public defense!