Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912911238103040 |
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| author | Shahbazi, Marzieh Amiri Baheri, Ali |
| author_facet | Shahbazi, Marzieh Amiri Baheri, Ali |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16015 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifolds Shahbazi, Marzieh Amiri Baheri, Ali Machine Learning 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. |
| title | Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifolds |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.16015 |