Uncertainty quantification is essential in decision-making, especially when joint distributions of random variables are involved. While conformal prediction provides distribution-free prediction sets with valid coverage guarantees, it traditionally focuses on single predictions. This paper introduces novel conformal prediction methods for estimating the sum or average of unknown labels over specific index sets. We develop conformal prediction intervals for single target to the prediction interval for sum of multiple targets. Under permutation invariant assumptions, we prove the validity of our proposed method. We also apply our algorithms on class average estimation and path cost prediction tasks, and we show that our method outperforms existing conformalized approaches as well as non-conformal approaches.

翻译：不确定性量化在决策过程中至关重要，特别是在涉及随机变量联合分布的场景下。虽然保形预测能够提供具有有效覆盖保证的分布无关预测集，但传统方法主要关注单一预测。本文针对特定索引集上未知标签之和或平均值的估计问题，提出了新颖的保形预测方法。我们将单目标预测区间扩展至多目标求和的预测区间。在置换不变的假设条件下，我们证明了所提方法的有效性。通过类别平均估计与路径成本预测任务的实验验证，本方法在保形化及非保形化方案中均展现出更优性能。