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This research addresses a critical gap in conformal prediction by adapting uncertainty quantification for Riemannian manifolds, ensuring that prediction intervals respect the intrinsic geometry of the data rather than relying on flawed Euclidean approximations. By utilizing geodesic distances and cross-validated normalization, the proposed framework achieves robust marginal coverage and reduced variation in conditional coverage across both synthetic and real-world forecasting tasks. This advancement is particularly relevant for machine learning applications involving spherical data or other non-Euclidean output spaces where standard error metrics fail to capture meaningful uncertainty.
Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifolds
arXiv:2602.16015v2 Announce Type: replace Abstract: Conformal prediction gives finite-sample coverage guarantees for regression, but most standard constructions are designed for Euclidean output spaces. When the response lies on a Riemannian manifold, Euclidean residuals and coordinate-based regions can ignore the geometry that defines meaningful error. We propose adaptive geodesic conformal prediction, a simple framework that builds nonconformity scores from geodesic distances and normalizes them with a cross-validated estimate of local prediction difficulty. On the sphere, this produces geodesic caps whose area is independent of position, while their radii still adapt to heteroscedastic noise. In both a synthetic sphere experiment and an IGRF-14 geomagnetic field forecasting task, the adaptive method preserves valid marginal coverage, reduces variation in conditional coverage, and improves worst-case coverage relative to non-adaptive and coordinate-based baselines.
Abstract:Conformal prediction gives finite-sample coverage guarantees for regression, but most standard constructions are designed for Euclidean output spaces. When the response lies on a Riemannian manifold, Euclidean residuals and coordinate-based regions can ignore the geometry that defines meaningful error. We propose adaptive geodesic conformal prediction, a simple framework that builds nonconformity scores from geodesic distances and normalizes them with a cross-validated estimate of local prediction difficulty. On the sphere, this produces geodesic caps whose area is independent of position, while their radii still adapt to heteroscedastic noise. In both a synthetic sphere experiment and an IGRF-14 geomagnetic field forecasting task, the adaptive method preserves valid marginal coverage, reduces variation in conditional coverage, and improves worst-case coverage relative to non-adaptive and coordinate-based baselines.
Machine Learning (cs.LG)
arXiv:2602.16015 [cs.LG]
(or arXiv:2602.16015v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2602.16015 Focus to learn more arXiv-issued DOI via DataCite
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