Data-driven selection or combination of Grassmannian metrics

Develop data-driven procedures for selecting or combining Grassmannian distance metrics within adaptive conformal prediction.

Background

The paper evaluates geodesic, projection, Procrustes, and Binet–Cauchy distances and shows that metric choice can affect statistical efficiency while preserving marginal validity. The authors leave unresolved the problem of choosing or combining these metrics in a data-driven manner rather than specifying them in advance.

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