Multivariate Conformal Prediction using Optimal Transport

Michal Klein, Louis Béthune, Eugene Ndiaye, marco cuturi

TL;DR: Multivariate Conformal Prediction using Optimal Transport

Abstract: onformal prediction quantifies the uncertainty of machine learning models by constructing sets of plausible outputs instead of relying on a single prediction, which may not exactly match the ground-truth. This is achieved by evaluating all possible output candidates and selecting the most likely ones by ranking their score functions, which measure how well each candidate aligns with the given input, the prediction model, and past observations. Traditionally, this approach has been limited to univariate score functions, as ranking requires a scalar value to order candidates. The challenge lies in extending ranking to multivariate spaces, where no canonical order exists. To address this, we leverage a natural extension of multivariate score ranking based on optimal transport mappings. Our method offers a principled framework for constructing conformal prediction sets in multidimensional settings, preserving distribution-free coverage guarantees with finite data samples.

Primary Area: Probabilistic Methods

Keywords: Uncertainty, Optimal Transport, Conformal Prediction

Submission Number: 15900