# Optimal Transport-based Conformal Prediction

arXiv: https://arxiv.org/abs/2501.18991 · HTML: https://mlsanity.com/paper/2501.18991/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 53 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 22 of 22)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Probabilistic Conformal Prediction Using Conditional Random Samples](https://mlsanity.com/paper/2206.06584/) (2022)
- [Exchangeability, Conformal Prediction, and Rank Tests](https://mlsanity.com/paper/2005.06095/) (2020)
- [Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportation](https://mlsanity.com/paper/1909.08733/) (2019)
- [Probabilistic Conformal Prediction with Approximate Conditional Validity](https://mlsanity.com/paper/2407.01794/) (2024)
- [Semiparametric conformal prediction](https://mlsanity.com/paper/2411.02114/) (2024)
- [Fast Nonlinear Vector Quantile Regression](https://mlsanity.com/paper/2205.14977/) (2022)
- [Nonparametric Multiple-Output Center-Outward Quantile Regression](https://mlsanity.com/paper/2204.11756/) (2022)
- [Max-Rank: Efficient Multiple Testing for Conformal Prediction](https://mlsanity.com/paper/2311.10900/) (2023)
- [The Penalized Inverse Probability Measure for Conformal Classification](https://mlsanity.com/paper/2406.08884/) (2024)
- [Multivariate quantile-based permutation tests with application to functional data](https://mlsanity.com/paper/2311.04017/) (2023)

## Built on by (most cited first, 20 of 20)

- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Conditional Coverage Diagnostics for Conformal Prediction](https://mlsanity.com/paper/2512.11779/) (2025)
- [Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regression](https://mlsanity.com/paper/2503.02205/) (2025)
- [Multivariate Standardized Residuals for Conformal Prediction](https://mlsanity.com/paper/2507.20941/) (2025)
- [Flow-based Conformal Prediction for Multi-dimensional Time Series](https://mlsanity.com/paper/2502.05709/) (2025)
- [Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settings](https://mlsanity.com/paper/2511.15146/) (2025)
- [Neural Optimal Transport Meets Multivariate Conformal Prediction](https://mlsanity.com/paper/2509.25444/) (2025)
- [Interpretable Multivariate Conformal Prediction with Fast Transductive Standardization](https://mlsanity.com/paper/2512.15383/) (2025)
- [Conformal Prediction for Generative Models via Adaptive Cluster-Based Density Estimation](https://mlsanity.com/paper/2601.22298/) (2026)
- [Conformal Graph Prediction with Z-Gromov-Wasserstein Distances](https://mlsanity.com/paper/2603.02460/) (2026)
- [Scalable and adaptive prediction bands with kernel sum-of-squares](https://mlsanity.com/paper/2505.21039/) (2025)
- [Multidimensional Uncertainty Quantification via Optimal Transport](https://mlsanity.com/paper/2509.22380/) (2025)
- [Minimax Multi-Target Conformal Prediction with Applications to Imaging Inverse Problems](https://mlsanity.com/paper/2511.13533/) (2025)
- [A Kernel Nonconformity Score for Multivariate Conformal Prediction](https://mlsanity.com/paper/2604.21595/) (2026)
- [Shape-Adaptive Conditional Calibration for Conformal Prediction via Minimax Optimization](https://mlsanity.com/paper/2603.23374/) (2026)
- [Super-Level-Set Regression: Conditional Quantiles via Volume Minimization](https://mlsanity.com/paper/2605.06210/) (2026)
- [Manifold Constrained Conformal Prediction for Spatial Events](https://mlsanity.com/paper/2607.10008/) (2026)
- [Tail-Aware Geometry Learning for Conformal Ellipsoids](https://mlsanity.com/paper/2609.27221/) (2026)
- [Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfalls](https://mlsanity.com/paper/2609.31384/) (2026)

## Abstract (arXiv)

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.