Metric Conformal Prediction via the Conditional Expected Local Radius
Abstract
We introduce the conditional expected local radius (CELR) and develop a new conformal prediction method for non-Euclidean responses in general metric spaces. CELR measures local conditional probability concentration, allowing prediction sets to accommodate heterogeneity and multimodality without requiring densities or a vector space structure. Its conditional distribution yields a nonconformity score that is comparable across covariate values and avoids costly transport comparisons between distance profiles. We further adapt a metric distributional random forest that handles multivariate covariates and nonlinear interactions, while a single forest fit supplies all score components, reducing computation by eliminating repeated local fitting. We establish uniform consistency of the estimators and asymptotic conditional validity under suitable regularity conditions, together with finite-sample marginal coverage under exchangeability. Numerical studies demonstrate effective uncertainty quantification across different metric spaces and substantial computational savings over the conditional profile score method.
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BibTeX
@misc{qiu2026metric,
title = {{Metric Conformal Prediction via the Conditional Expected Local Radius}},
author = {Rui Qiu and Fang Yao and Zhou Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31336},
eprint = {2610.31336},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31336},
}
RIS
TY - UNPB
TI - Metric Conformal Prediction via the Conditional Expected Local Radius
AU - Rui Qiu
AU - Fang Yao
AU - Zhou Yu
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.31336
UR - https://arxiv.org/abs/2610.31336
AB - We introduce the conditional expected local radius (CELR) and develop a new conformal prediction method for non-Euclidean responses in general metric spaces. CELR measures local conditional probability concentration, allowing prediction sets to accommodate heterogeneity and multimodality without requiring densities or a vector space structure. Its conditional distribution yields a nonconformity score that is comparable across covariate values and avoids costly transport comparisons between distance profiles. We further adapt a metric distributional random forest that handles multivariate covariates and nonlinear interactions, while a single forest fit supplies all score components, reducing computation by eliminating repeated local fitting. We establish uniform consistency of the estimators and asymptotic conditional validity under suitable regularity conditions, together with finite-sample marginal coverage under exchangeability. Numerical studies demonstrate effective uncertainty quantification across different metric spaces and substantial computational savings over the conditional profile score method.
ER -