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arXiv · 2610.23508

Adaptive conformal prediction on the Grassmannian

Dimitrios Loukrezis·Zachary J. Grey·Dimitris G. Giovanis
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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.

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Dimitrios Loukrezis, Zachary J. Grey, Dimitris G. Giovanis. 2026-10-16. Adaptive conformal prediction on the Grassmannian. https://arxiv.org/abs/2610.23508

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