[Statlist] Research Seminar in Statistics | *FRIDAY 16 October 2026* | GSEM, University of Geneva

[gsem-support-instituts]

Dear Dr Santoro,

We are pleased to invite you to our next Research Seminar, organized by Professor Jeffrey Näf on behalf of the Research Institute for Statistics and Information Science
< https://www.unige.ch/gsem/en/research/institutes/risis/team/ >.

FRIDAY 16 October 2026, at 11:15 am, Uni Mail M 5220.

>From Separation to Transport: Second-Order Kernel Methods
Leonardo SANTORO, EPFL, Switzerland
< https://people.epfl.ch/leonardo.santoro?lang=en >

ABSTRACT:
Kernel methods provide a powerful way to represent data distributions. We argue that their full potential can be understood through second-order embeddings, equipped with a geometry appropriate to the task at hand. For distributional inference, an information-theoretic perspective leads to a striking separation-of-measures phenomenon: distinct distributions are mapped to mutually singular Gaussian embeddings in the kernel space. This yields a likelihood-ratio interpretation of kernel two-sample testing and provides a unified view of several classical methods. This representational richness extends beyond testing to generative sampling, which calls for a geometry capturing the transport structure between distributions. We use the Bures-Wasserstein geometry of Gaussian embeddings to construct a neural-network-free framework for generative sampling. The resulting closed-form geodesic induces an affine velocity field in the RKHS, which we pull back to the data space to obtain an explicit transport map. A geometric diagnostic then allows the velocity field to be iteratively refined. Together, these results illustrate how second-order kernel embeddings, combined with task-specific geometries, can provide a common framework for statistical inference and generative modeling.

> View the Research Seminar agenda: < https://www.unige.ch/gsem/en/research/seminars/risis/ >

With kind regards,


Birgit Müller-Marreros 
Assistant to the Research Institutes
Mail.unige.ch

GSEM Support for Research Institutes
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