ICML 2025

Optimal Transport-based Conformal Prediction
Gauthier Thurin 1 Kimia Nadjahi 1 Claire Boyer 2
Abstract
Conformal Prediction (CP) is a principled frame-
work for quantifying uncertainty in black-box
learning models, by constructing prediction sets
with finite-sample coverage guarantees. Tradi-
tional 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. Re-
cent methods addressing this limitation impose
predefined convex shapes for the prediction sets,
potentially misaligning with the intrinsic data ge-
ometry. We introduce a novel CP procedure hand-
ling multivariate score functions through the lens
of optimal transport. Specifically, we leverage
Monge-Kantorovich vector ranks and quantiles to
construct prediction region with flexible, poten-
tially non-convex shapes, better suited to the com-
plex uncertainty patterns encountered in multivari-
ate 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 predic-
tion 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.
1. Introduction
In various domains, including high-stakes applications,
state-of-the-art performances are often achieved by black-
box machine learning models. As a result, accurately quan-
tifying the uncertainty of their predictions has become a crit-
1CNRS, Ecole Normale Sup´erieure, Paris, France 2Laboratoire
de Math´ematiques d’Orsay (LMO), Universit´e Paris Saclay,
France, and Institut universitaire de France. Correspondence to:
Gauthier Thurin <gthurin@mail.di.ens.fr>.
Proceeding...