Seminar

Optimal Transport-based Conformal Prediction

19/11/2025

Title

Speaker

Kimia Nadjahi - ENS Paris

Abstract

Conformal Prediction (CP) is a principled framework for quantifying uncertainty in black-box learning models, by constructing prediction sets with finite-sample coverage guarantees. Traditional approaches rely on scalar nonconformity scores, which fail to fully exploit the geometric structure of multivariate outputs, such as in multi-output regression or multiclass classification. Recent methods addressing this limitation impose predefined convex shapes for the prediction sets, potentially misaligning with the intrinsic data geometry. We introduce a novel CP procedure handling multivariate score functions through the lens of optimal transport. Specifically, we leverage Monge-Kantorovich vector ranks and quantiles to construct prediction regions with flexible, potentially non-convex shapes, better suited to the complex uncertainty patterns encountered in multivariate learning tasks. We prove that our approach ensures finite-sample, distribution-free coverage properties, similar to typical CP methods. We then adapt our method for multi-output regression and multiclass classification, and also propose simple adjustments to generate adaptive prediction regions with asymptotic conditional coverage guarantees. Finally, we evaluate our method on practical regression and classification problems, illustrating its advantages in terms of (conditional) coverage and efficiency. This talk is based on the following paper: "Optimal Transport-based Conformal Prediction" (ICML 2025) with Gauthier Thurin (CNRS, ENS) and Claire Boyer (Université Paris-Saclay).

Bio

Kimia Nadjahi is a CNRS researcher at ENS Paris, affiliated with the Computer Science department and Centre de Sciences des Données. Her research focuses on computational optimal transport and statistical learning theory. She has particular expertise in sliced optimal transport, a computationally efficient variant of standard optimal transport that leverages dimension reduction with random projections. She has also worked on the analysis of the generalization error in compressible deep learning models. Before joining CNRS, she was a postdoctoral fellow at MIT, and a postdoctoral researcher at Sorbonne University. She received her PhD from Telecom Paris and Institut Polytechnique de Paris.

When

Wednesday, November 19th, 14:00

Where

Room 322, UniGe DIBRIS/DIMA, Via Dodecaneso 35