# Conformal Prediction for Ensembles: Improving Efficiency via Score-Based Aggregation

arXiv: https://arxiv.org/abs/2405.16246 · HTML: https://mlsanity.com/paper/2405.16246/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 54 references that are in the map.
- First posted on arXiv 25 May 2024.

## Builds on (most cited first, 17 of 17)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Training independent subnetworks for robust prediction](https://mlsanity.com/paper/2010.06610/) (2020)
- [Uncertainty Quantification and Deep Ensembles](https://mlsanity.com/paper/2007.08792/) (2020)
- [PreDiff: Precipitation Nowcasting with Latent Diffusion Models](https://mlsanity.com/paper/2307.10422/) (2023)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Selection and Aggregation of Conformal Prediction Sets](https://mlsanity.com/paper/2104.13871/) (2021)
- [Conformal Prediction Sets Improve Human Decision Making](https://mlsanity.com/paper/2401.13744/) (2024)
- [Merging uncertainty sets via majority vote](https://mlsanity.com/paper/2401.09379/) (2024)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [UNO: Uncertainty-aware Noisy-Or Multimodal Fusion for Unanticipated Input Degradation](https://mlsanity.com/paper/1911.05611/) (2019)
- [Predict-then-Calibrate: A New Perspective of Robust Contextual LP](https://mlsanity.com/paper/2305.15686/) (2023)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)
- [Conformal online model aggregation](https://mlsanity.com/paper/2403.15527/) (2024)

## Built on by (most cited first, 9 of 9)

- [ReconVLA: An Uncertainty-Guided and Failure-Aware Vision-Language-Action Framework for Robotic Control](https://mlsanity.com/paper/2604.16677/) (2026)
- [Symmetric Aggregation of Conformity Scores for Efficient Uncertainty Sets](https://mlsanity.com/paper/2512.06945/) (2025)
- [CAOS: Conformal Aggregation of One-Shot Predictors](https://mlsanity.com/paper/2601.05219/) (2026)
- [Empirical Bayes Conformal Prediction for Vision and Language Models](https://mlsanity.com/paper/2605.23189/) (2026)
- [Enhancing Decision-Making in Windows PE Malware Classification During Dataset Shifts with Uncertainty Estimation](https://mlsanity.com/paper/2512.18495/) (2025)
- [Conformalized Super Learner](https://mlsanity.com/paper/2604.22391/) (2026)
- [Soft Specialists: α-R'enyi Ensembles for Uncertainty-Aware LLM Post-Training](https://mlsanity.com/paper/2605.27747/) (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)

Distribution-free uncertainty estimation for ensemble methods is increasingly desirable due to the widening deployment of multi-modal black-box predictive models. Conformal prediction is one approach that avoids such distributional assumptions. Methods for conformal aggregation have in turn been proposed for ensembled prediction, where the prediction regions of individual models are merged as to retain coverage guarantees while minimizing conservatism. Merging the prediction regions directly, however, sacrifices structures present in the conformal scores that can further reduce conservatism. We, therefore, propose a novel framework that extends the standard scalar formulation of a score function to a multivariate score that produces more efficient prediction regions. We then demonstrate that such a framework can be efficiently leveraged in both classification and predict-then-optimize regression settings downstream and empirically show the advantage over alternate conformal aggregation methods.