Nonparametric two-sample testing with permutations, kernels and optimal transport.

Title

Nonparametric two-sample testing with permutations, kernels and optimal transport.

Speaker

Nicolas Schreuder - CNRS

Abstract

Two-sample testing is a classical problem in statistics: given two datasets, can we determine whether they originate from the same distribution? While traditional methods often rely on strong parametric assumptions or are limited to low-dimensional settings, the development of flexible metrics on the space of probability distributions—such as those based on kernels and optimal transport—has enabled the design of nonparametric tests with both statistical and computational advantages, broadening applicability to more complex data. In this talk, I will introduce the framework of two-sample testing and explain how a permutation trick can be used to construct valid tests under only exchangeability or i.i.d. assumptions. I will then present recent results from my work on developing and analyzing permutation-based two-sample tests, using the sliced Wasserstein distance and efficient approximations of the Maximum Mean Discrepancy (MMD).

This talk is based on the following works:

• A Scalable Nyström-Based Kernel Two-Sample Test with Permutations, with Antoine Chatalic, Marco Letizia, and Lorenzo Rosasco. arXiv:2502.13570, 2024.

• Minimax-Optimal Two-Sample Test with Sliced Wasserstein, with Binh Thuan Tran. Preprint to appear on arXiv.

Bio

Nicolas Schreuder is a CNRS research scientist (“chargé de recherche”) at the Laboratoire d’Informatique Gaspard-Monge (LIGM). His research lies at the intersection of statistical learning and machine learning, with a focus on fairness and, more broadly, on the design and analysis of trustworthy learning algorithms. Before joining CNRS, he was a postdoctoral researcher with Lorenzo Rosasco at the Università di Genova. He earned his PhD in Statistics from CREST and Institut Polytechnique de Paris, under the supervision of Arnak Dalalyan and Victor-Emmanuel Brunel.

When

Wednesday, October 15th, 14:30

Where

Room 217, UniGe DIBRIS/DIMA, Via Dodecaneso 35