Optimal Transport-based Conformal Prediction

TL;DR

This paper introduces a new conformal prediction method using optimal transport to create flexible, non-convex prediction regions for multivariate outputs, improving uncertainty quantification in complex learning tasks.

Contribution

It develops an optimal transport-based conformal prediction framework that constructs adaptable, non-convex prediction sets with finite-sample coverage guarantees for multivariate models.

Findings

Improved coverage and efficiency in multivariate prediction tasks.

Flexible prediction regions better aligned with data geometry.

Finite-sample, distribution-free coverage guarantees achieved.

Abstract

Conformal Prediction (CP) is a principled framework for quantifying uncertainty in blackbox 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 region 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.