![[2602.16015] Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifolds](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2602.16015] Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifolds
Summary
This paper introduces adaptive geodesic conformal prediction, a novel framework for uncertainty quantification on Riemannian manifolds, enhancing prediction accuracy in complex data environments.
Why It Matters
The research addresses limitations in existing conformal prediction methods that assume Euclidean spaces, which can lead to poor calibration in manifold contexts. By improving uncertainty quantification, this work has implications for fields like geoscience and machine learning, where accurate predictions are crucial.
Key Takeaways
- Introduces adaptive geodesic conformal prediction for better uncertainty quantification.
- Replaces Euclidean residuals with geodesic nonconformity scores for improved calibration.
- Demonstrates significant improvements in conditional coverage in both synthetic and real-world scenarios.
- Addresses heteroscedastic noise effectively, adapting prediction regions to local difficulties.
- Provides a framework applicable to various fields, enhancing predictive modeling capabilities.
Computer Science > Machine Learning arXiv:2602.16015 (cs) [Submitted on 17 Feb 2026] Title:Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifolds Authors:Marzieh Amiri Shahbazi, Ali Baheri View a PDF of the paper titled Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifolds, by Marzieh Amiri Shahbazi and Ali Baheri View PDF HTML (experimental) 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...
