Statistics > Machine Learning
arXiv:2502.03609 (stat)
[Submitted on 5 Feb 2025]
Title:Multivariate Conformal Prediction using Optimal Transport
View a PDF of the paper titled Multivariate Conformal Prediction using Optimal Transport, by Michal Klein and Louis Bethune and Eugene Ndiaye and Marco Cuturi
View PDFHTML (experimental)Abstract:Conformal prediction (CP) quantifies the uncertainty of machine learning models by constructing sets of plausible outputs. These sets are constructed by leveraging a so-called conformity score, a quantity computed using the input point of interest, a prediction model, and past observations. CP sets are then obtained by evaluating the conformity score of all possible outputs, and selecting them according to the rank of their scores. Due to this ranking step, most CP approaches rely on a score functions that are univariate. The challenge in extending these scores to multivariate spaces lies in the fact that no canonical order for vectors exists. To address this, we leverage a natural extension of multivariate score ranking based on optimal transport (OT). Our method, OTCP, offers a principled framework for constructing conformal prediction sets in multidimensional settings, preserving distribution-free coverage guarantees with finite data samples. We demonstrate tangible gains in a benchmark dataset of multivariate regression problems and address computational \& statistical trade-offs that arise when estimating conformity scores through OT maps.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2502.03609 [stat.ML] |
| (orarXiv:2502.03609v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2502.03609 arXiv-issued DOI via DataCite |
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View a PDF of the paper titled Multivariate Conformal Prediction using Optimal Transport, by Michal Klein and Louis Bethune and Eugene Ndiaye and Marco Cuturi
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