While split conformal prediction guarantees marginal coverage, approaching the stronger property of conditional coverage is essential for reliable uncertainty quantification. Naive conformal scores, however, suffer from poor conditional coverage in heteroskedastic settings. In univariate regression, this is commonly addressed by normalizing nonconformity scores using estimated local score variance. In this work, we propose a natural extension of this normalization to the multivariate setting, effectively whitening the residuals to decouple output correlations and standardize local variance. We demonstrate that using the Mahalanobis distance induced by a learned local covariance as a nonconformity score provides a closed-form, computationally efficient mechanism for capturing inter-output correlations and heteroskedasticity, avoiding the expensive sampling required by previous methods based on cumulative distribution functions. This structure unlocks several practical extensions, including the handling of missing output values, the refinement of conformal sets when partial information is revealed, and the construction of valid conformal sets for transformations of the output. Finally, we provide extensive empirical evidence on both synthetic and real-world datasets showing that our approach yields conformal sets that significantly improve upon the conditional coverage of existing multivariate baselines.

翻译：尽管分割共形预测能够保证边缘覆盖，但逼近条件覆盖这一更强性质对于可靠的不确定性量化至关重要。然而，在异方差场景中，朴素的共形得分往往表现出较差的条件覆盖性能。在单变量回归中，通常通过使用估计的局部得分方差对非共形得分进行归一化来解决此问题。本文中，我们提出将该归一化方法自然地扩展到多元场景，通过有效白化残差以解耦输出相关性并标准化局部方差。我们证明，使用由学习到的局部协方差矩阵诱导的马氏距离作为非共形得分，能够提供一种闭式、计算高效的机制来捕捉输出间相关性与异方差性，从而避免以往基于累积分布函数的方法所需的高昂采样成本。这一结构启发了若干实用扩展，包括处理缺失输出值、在部分信息已知时优化共形集，以及为输出变换构建有效的共形集。最后，我们在合成数据集和真实数据集上提供了充分的实证证据，表明我们的方法生成的共形集在条件覆盖性能上显著优于现有的多元基线方法。