发表机构
Nanyang Technological University（南洋理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种尾部感知的共形椭球几何学习框架，通过两分割设计解耦尾部敏感性与覆盖保证，在CVaR约束下最小化体积，实现高效且鲁棒的多元预测集。
AI 中文摘要
本文研究多元共形预测（CP），这是一种具有有限样本覆盖保证的无分布不确定性量化框架。多元预测集的效率关键取决于由非共形分数编码的残差几何，而现有的最小体积方法依赖于分位数阈值，该阈值忽略了尾部残差的严重性，并隐含地将几何学习与覆盖水平绑定。我们提出了一种面向共形椭球的尾部感知几何学习框架，该框架将几何学习中的尾部敏感性与最终覆盖保证解耦。通过两分割设计，我们在估计分割上通过CVaR约束下的体积最小化来学习度量矩阵，然后在保留的校准分割上应用标准共形校准。由此产生的问题是凸的，并允许有界重加权解释，该解释优先考虑高残差样本。此外，我们从理论上刻画了椭球体积与尾部严重性之间的权衡。实验结果表明了所提方法的有效性。
英文摘要
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.
