Alternative local geometric-difficulty estimators

Develop and evaluate alternative estimators of local geometric prediction difficulty for adaptive conformal prediction on the Grassmann manifold.

Background

The method estimates local prediction difficulty using a regression model trained on cross-validation geometric residuals after a logarithmic transformation. Because the framework is model-agnostic, other estimators could potentially produce better local scaling and more efficient adaptive regions. The authors explicitly list alternative local geometric-difficulty estimators among the unresolved extensions.

References

Several directions remain open. The equivalent-radius and volume measures were used in this work to provide a practical normalization for comparing different Grassmannian metrics, but their extension to exact anisotropic prediction-set volumes in higher-dimensional Grassmannians would enable more precise efficiency comparisons. Locally anisotropic conformal regions whose geometry adapts not only in radius but also along different tangent directions, may further improve efficiency when uncertainty is strongly directional. Other extensions include alternative estimators of local geometric difficulty, data-driven selection or combination of Grassmannian metrics, and conformal methods designed for weaker forms of exchangeability or distribution shift.

— Adaptive conformal prediction on the Grassmannian  (2610.23508 - Loukrezis et al., 16 Oct 2026) in Section 7, Conclusions