Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifolds

• URL: http://arxiv.org/abs/2602.16015v1
• Date: Tue, 17 Feb 2026 21:12:47 GMT
• Title: Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifolds
• Authors: Marzieh Amiri Shahbazi, Ali Baheri,
• Abstract summary: We propose a framework that replaces Euclidean residuals with geodesic nonconformity scores and normalizes them by a cross-validated difficulty estimator to handle heteroscedastic noise.<n>The resulting prediction regions, geodesic caps on the sphere, have position-independent area and adapt their size to local prediction difficulty, yielding substantially more uniform conditional coverage than non-adaptive alternatives.
• Score: 3.2848713528308817
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Conformal prediction provides distribution-free coverage guaranties for regression; yet existing methods assume Euclidean output spaces and produce prediction regions that are poorly calibrated when responses lie on Riemannian manifolds. We propose \emph{adaptive geodesic conformal prediction}, a framework that replaces Euclidean residuals with geodesic nonconformity scores and normalizes them by a cross-validated difficulty estimator to handle heteroscedastic noise. The resulting prediction regions, geodesic caps on the sphere, have position-independent area and adapt their size to local prediction difficulty, yielding substantially more uniform conditional coverage than non-adaptive alternatives. In a synthetic sphere experiment with strong heteroscedasticity and a real-world geomagnetic field forecasting task derived from IGRF-14 satellite data, the adaptive method markedly reduces conditional coverage variability and raises worst-case coverage much closer to the nominal level, while coordinate-based baselines waste a large fraction of coverage area due to chart distortion.

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