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.

CASCADE Conformal Prediction: Uncertainty-Adaptive Prediction Intervals for Two-Stage Clinical Decision Support
Ricardo Diaz-Rincon, Muxuan Liang, Adolfo Ramirez-Zamora +1
arXiv30 Sep 2026PreprintCC BY 4.0Full textStatisticsarXiv
Skew-adaptive conformal prediction
Paulo C. Marques F., Helton Graziadei
arXiv15 May 2026PreprintarXiv licenceFull textStatisticsarXiv
Adaptive Conformal Prediction for Image Regression Models with Application to an Inertial Confinement Fusion Emulator
Carrie J. Lei-Cramer, Michael S. Jones, Laura J. Wendelberger
arXiv1 Oct 2026PreprintarXiv licenceFull textStatisticsarXiv
Beyond Imputation: Mask-Adaptive Conformal Prediction via Tree Embeddings on General Missing Data Mechanisms
Jiarong Fan, Juhyun Park, Thi Phuong Thuy Vo +1
arXiv1 Nov 2026PreprintCC BY 4.0Full textStatisticsarXiv
The Conformal Grassmannian: A Symplectic Bi-Grassmannian for CFT₄ Correlators
Aswini Bala, Sachin Jain, Dhruva K. S
arXiv15 Sep 2026PreprintCC0Full textMathematical physics High-energy & particle physicsarXiv

Cite

BibTeX RIS

BibTeX

@misc{loukrezis2026adaptive,
  title = {{Adaptive conformal prediction on the Grassmannian}},
  author = {Dimitrios Loukrezis and Zachary J. Grey and Dimitris G. Giovanis},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23508},
  eprint = {2610.23508},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23508},
  note = {CC BY-NC-ND 4.0},
}

RIS

TY  - UNPB
TI  - Adaptive conformal prediction on the Grassmannian
AU  - Dimitrios Loukrezis
AU  - Zachary J. Grey
AU  - Dimitris G. Giovanis
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23508
UR  - https://arxiv.org/abs/2610.23508
AB  - 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.
ER  -

Abstract

Related

Cite