aiqbench analysis
This research advances multivariate conformal prediction by introducing a tail-aware geometry learning framework that decouples residual sensitivity from coverage guarantees. By optimizing the metric matrix under Conditional Value-at-Risk constraints, the method prioritizes high-residual samples to improve efficiency without compromising finite-sample validity. The approach offers a convex formulation with theoretical trade-off characterizations, providing a robust tool for uncertainty quantification in complex multivariate settings.
Tail-Aware Geometry Learning for Conformal Ellipsoids
arXiv:2609.27221v1 Announce Type: new Abstract: This paper studies multivariate conformal prediction (CP), a distribution-free uncertainty quantification framework with finite-sample coverage guarantees. The efficiency of multivariate prediction sets hinges critically on the residual geometry encoded by the nonconformity score, while existing minimum-volume methods rely on quantile thresholds that ignore tail residual severity and implicitly bind geometry learning to coverage level. We propose a tail-aware geometry learning framework for conformal ellipsoids that decouples tail sensitivity in geometry learning from the final coverage guarantee. Using a two-split design, we learn the metric matrix via volume minimization under a CVaR constraint on an estimation split, then apply standard conformal calibration on a held-out calibration split. The resulting problem is convex and admits a bounded-reweighting interpretation that prioritizes high-residual samples. Moreover, we theoretically characterize the trade-off between ellipsoidal volume and tail severity. Experimental results demonstrate the effectiveness of the proposed method.
Abstract:This paper studies multivariate conformal prediction (CP), a distribution-free uncertainty quantification framework with finite-sample coverage guarantees. The efficiency of multivariate prediction sets hinges critically on the residual geometry encoded by the nonconformity score, while existing minimum-volume methods rely on quantile thresholds that ignore tail residual severity and implicitly bind geometry learning to coverage level. We propose a tail-aware geometry learning framework for conformal ellipsoids that decouples tail sensitivity in geometry learning from the final coverage guarantee. Using a two-split design, we learn the metric matrix via volume minimization under a CVaR constraint on an estimation split, then apply standard conformal calibration on a held-out calibration split. The resulting problem is convex and admits a bounded-reweighting interpretation that prioritizes high-residual samples. Moreover, we theoretically characterize the trade-off between ellipsoidal volume and tail severity. Experimental results demonstrate the effectiveness of the proposed method.
Machine Learning (cs.LG)
arXiv:2609.27221 [cs.LG]
(or arXiv:2609.27221v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.27221 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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