# Symmetric Aggregation of Conformity Scores for Efficient Uncertainty Sets

arXiv: https://arxiv.org/abs/2512.06945 · HTML: https://mlsanity.com/paper/2512.06945/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 7 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Merging uncertainty sets via majority vote](https://mlsanity.com/paper/2401.09379/) (2024)
- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [E-Values Expand the Scope of Conformal Prediction](https://mlsanity.com/paper/2503.13050/) (2025)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Trustworthy Classification through Rank-Based Conformal Prediction Sets](https://mlsanity.com/paper/2407.04407/) (2024)
- [Enhancing Conformal Prediction Using E-Test Statistics](https://mlsanity.com/paper/2403.19082/) (2024)
- [From Aleatoric to Epistemic: Exploring Uncertainty Quantification Techniques in Artificial Intelligence](https://mlsanity.com/paper/2501.03282/) (2025)
- [Conformal Prediction for Ensembles: Improving Efficiency via Score-Based Aggregation](https://mlsanity.com/paper/2405.16246/) (2024)
- [Improving the statistical efficiency of cross-conformal prediction](https://mlsanity.com/paper/2503.01495/) (2025)

## Built on by (most cited first, 4 of 4)

- [CAOS: Conformal Aggregation of One-Shot Predictors](https://mlsanity.com/paper/2601.05219/) (2026)
- [Improving Backward Conformal Prediction via Non-Conformity Score Transformation](https://mlsanity.com/paper/2602.01733/) (2026)
- [Set-Preserving Calibration from Conformal P-Values to E-Values](https://mlsanity.com/paper/2606.03600/) (2026)
- [Unifying Conformal Language Tasks with In-Context Ensembles](https://mlsanity.com/paper/2609.03005/) (2026)

## Abstract (arXiv)

Access to multiple predictive models trained for the same task, whether in regression or classification, is increasingly common in many applications. Aggregating their predictive uncertainties to produce reliable and efficient uncertainty quantification is therefore a critical but still underexplored challenge, especially within the framework of conformal prediction (CP). While CP methods can generate individual prediction sets from each model, combining them into a single, more informative set remains a challenging problem. To address this, we propose SACP (Symmetric Aggregated Conformal Prediction), a novel method that aggregates nonconformity scores from multiple predictors. SACP transforms these scores into e-values and combines them using any symmetric aggregation function. This flexible design enables a robust, data-driven framework for selecting aggregation strategies that yield sharper prediction sets. We also provide theoretical insights that help justify the validity and performance of the SACP approach. Extensive experiments on diverse datasets show that SACP consistently improves efficiency and often outperforms state-of-the-art model aggregation baselines.