Conformalized Interval Arithmetic with Symmetric Calibration

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.