Adaptive conformal prediction on the Grassmannian

Abstract:We introduce a conformal prediction framework for regression with Grassmann-valued responses. The proposed method constructs prediction regions in the form of metric balls directly on the Grassmann manifold, using basis-invariant geometric distances as non-conformity measures and scaling the corresponding non-conformity scores through a learned prediction difficulty estimator. This yields locally adaptive, input-dependent prediction regions that respect the underlying manifold geometry, while retaining the finite-sample marginal coverage guarantee of split conformal prediction under exchangeability. We evaluate several Grassmannian distance metrics and compare their prediction-region efficiency on synthetic benchmarks and an airfoil inverse shape-design problem. The results highlight the advantages of geometry-aware non-conformity scores, while local adaptation improves empirical coverage uniformity across prediction difficulty levels and, in strongly heteroscedastic settings, can substantially reduce prediction-region size while maintaining the target coverage.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2610.23508 [stat.ML]

(or arXiv:2610.23508v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.23508 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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