Conformal Prediction via Transported Beta Laws
Abstract
Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a realized conformal threshold. In the continuous i.i.d. setting this law is exactly Beta(k,n+1−k), so the usual marginal guarantee corresponds to its mean. We take this beta law as a finite-sample reference object and quantify departures from it using Wasserstein distances on [0,1]. The framework yields direct bounds on marginal coverage gaps and on bad-calibration probabilities, and separates different sources of non-i.i.d. behavior according to how they deform the beta reference: test-side shift acts through a transport map on the coverage scale, while calibration dependence changes the order-statistic law itself. We instantiate the framework in scale-shift, clustered, and stationary mixing settings, where the induced deformations can be characterized explicitly or through Berry-Esseen approximations. Simulations on dependent processes confirm that the first-order approximation tracks the empirical Wasserstein distance even at moderate sample sizes.
Related
- Poincaré Beta Balls: Radial Laws, Hyperbolic Shell Metric Transforms, and Critical-Limit Regimes
- Generalized Hyperrectangular Prediction Sets in Multivariate Conformal Prediction
- Conformal Prediction under Partial Verification
- Multi-Variable Conformal Prediction: Optimizing Prediction Sets using Multiple Calibration Variables
- Conformal Prediction and Conditional Coverage for Tabular Foundation Models
BibTeX
@misc{ramos2026conformal,
title = {{Conformal Prediction via Transported Beta Laws}},
author = {Thiago R. Ramos and Helton Graziadei and Luben M. C. Cabezas},
howpublished = {arXiv},
year = {2026},
month = may,
doi = {10.48550/arxiv.2605.19024},
eprint = {2605.19024},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.19024},
}
RIS
TY - UNPB
TI - Conformal Prediction via Transported Beta Laws
AU - Thiago R. Ramos
AU - Helton Graziadei
AU - Luben M. C. Cabezas
PY - 2026
DA - 2026/05/18
PB - arXiv
DO - 10.48550/arxiv.2605.19024
UR - https://arxiv.org/abs/2605.19024
AB - Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a realized conformal threshold. In the continuous i.i.d. setting this law is exactly Beta(k,n+1−k), so the usual marginal guarantee corresponds to its mean. We take this beta law as a finite-sample reference object and quantify departures from it using Wasserstein distances on [0,1]. The framework yields direct bounds on marginal coverage gaps and on bad-calibration probabilities, and separates different sources of non-i.i.d. behavior according to how they deform the beta reference: test-side shift acts through a transport map on the coverage scale, while calibration dependence changes the order-statistic law itself. We instantiate the framework in scale-shift, clustered, and stationary mixing settings, where the induced deformations can be characterized explicitly or through Berry-Esseen approximations. Simulations on dependent processes confirm that the first-order approximation tracks the empirical Wasserstein distance even at moderate sample sizes.
ER -