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.