# Conformalized Interval Arithmetic with Symmetric Calibration

arXiv: https://arxiv.org/abs/2408.10939 · HTML: https://mlsanity.com/paper/2408.10939/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 39 references that are in the map.
- First posted on arXiv 20 Aug 2024.

## Builds on (most cited first, 26 of 26)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [Fair Conformal Predictors for Applications in Medical Imaging](https://mlsanity.com/paper/2109.04392/) (2021)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Improving Conditional Coverage via Orthogonal Quantile Regression](https://mlsanity.com/paper/2106.00394/) (2021)
- [With Malice Towards None: Assessing Uncertainty via Equalized Coverage](https://mlsanity.com/paper/1908.05428/) (2019)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Trustworthy Classification through Rank-Based Conformal Prediction Sets](https://mlsanity.com/paper/2407.04407/) (2024)
- [Conformalized Fairness via Quantile Regression](https://mlsanity.com/paper/2210.02015/) (2022)
- [Anomalous Edge Detection in Edge Exchangeable Social Network Models](https://mlsanity.com/paper/2109.12727/) (2021)
- [Predict-then-Calibrate: A New Perspective of Robust Contextual LP](https://mlsanity.com/paper/2305.15686/) (2023)
- [Derandomized Novelty Detection with FDR Control via Conformal E-values](https://mlsanity.com/paper/2302.07294/) (2023)
- [Conformal Load Prediction with Transductive Graph Autoencoders](https://mlsanity.com/paper/2406.08281/) (2024)
- [Weighted Aggregation of Conformity Scores for Classification](https://mlsanity.com/paper/2407.10230/) (2024)
- [Conformal Thresholded Intervals for Efficient Regression](https://mlsanity.com/paper/2407.14495/) (2024)
- [Group-Conditional Conformal Prediction via Quantile Regression Calibration for Crop and Weed Classification](https://mlsanity.com/paper/2308.15094/) (2023)
- [Entropy Reweighted Conformal Classification](https://mlsanity.com/paper/2407.17377/) (2024)
- [Algorithms and Uncertainty Sets for Data-Driven Robust Shortest Path Problems](https://mlsanity.com/paper/1802.04149/) (2018)

## Built on by (most cited first, 8 of 8)

- [Conditional Conformal Risk Adaptation](https://mlsanity.com/paper/2504.07611/) (2025)
- [Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regression](https://mlsanity.com/paper/2503.02205/) (2025)
- [Enhancing Adversarial Robustness with Conformal Prediction: A Framework for Guaranteed Model Reliability](https://mlsanity.com/paper/2506.07804/) (2025)
- [Enhanced Route Planning with Calibrated Uncertainty Set](https://mlsanity.com/paper/2503.10088/) (2025)
- [Adaptive Conformal Inference by Particle Filtering under Hidden Markov Models](https://mlsanity.com/paper/2411.01558/) (2024)
- [Fast Conformal Prediction using Conditional Interquantile Intervals](https://mlsanity.com/paper/2601.02769/) (2026)
- [Residual Reweighted Conformal Prediction for Graph Neural Networks](https://mlsanity.com/paper/2506.07854/) (2025)
- [Simulation-Augmented Multi-Step Split Conformal Prediction for Aggregated Forecasts](https://mlsanity.com/paper/2606.16356/) (2026)

## Abstract (arXiv)

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.