# Valid Selection among Conformal Sets

arXiv: https://arxiv.org/abs/2506.20173 · HTML: https://mlsanity.com/paper/2506.20173/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 25 Jun 2025.

## Builds on (most cited first, 18 of 18)

- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Preserving Statistical Validity in Adaptive Data Analysis](https://mlsanity.com/paper/1411.2664/) (2014)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Algorithmic Stability for Adaptive Data Analysis](https://mlsanity.com/paper/1511.02513/) (2015)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Follow the Leader If You Can, Hedge If You Must](https://mlsanity.com/paper/1301.0534/) (2013)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Selection and Aggregation of Conformal Prediction Sets](https://mlsanity.com/paper/2104.13871/) (2021)
- [Achieving Risk Control in Online Learning Settings](https://mlsanity.com/paper/2205.09095/) (2022)
- [Merging uncertainty sets via majority vote](https://mlsanity.com/paper/2401.09379/) (2024)
- [Optimized Conformal Selection: Powerful Selective Inference After Conformity Score Optimization](https://mlsanity.com/paper/2411.17983/) (2024)
- [Conformal online model aggregation](https://mlsanity.com/paper/2403.15527/) (2024)
- [Multi-model Ensemble Conformal Prediction in Dynamic Environments](https://mlsanity.com/paper/2411.03678/) (2024)
- [Post-Selection Inference via Algorithmic Stability](https://mlsanity.com/paper/2011.09462/) (2020)

## Built on by (most cited first, 5 of 5)

- [Calibrating Decision Robustness via Inverse Conformal Risk Control](https://mlsanity.com/paper/2510.07750/) (2025)
- [CAOS: Conformal Aggregation of One-Shot Predictors](https://mlsanity.com/paper/2601.05219/) (2026)
- [Learning Polyhedral Conformal Sets for Robust Optimization](https://mlsanity.com/paper/2605.08506/) (2026)
- [Conformal Risk Sharing: Certified Cost Allocation with Participation Guarantees](https://mlsanity.com/paper/2606.06391/) (2026)
- [CopRoute: Dependence-Aware Conformal Routing for Language Models](https://mlsanity.com/paper/2610.13276/) (2026)

## Abstract (arXiv)

Conformal prediction offers a distribution-free framework for constructing prediction sets with coverage guarantees. In practice, multiple valid conformal prediction sets may be available, arising from different models or methodologies. However, selecting the most desirable set, such as the smallest, can invalidate the coverage guarantees. To address this challenge, we propose a stability-based approach that ensures coverage for the selected prediction set. We extend our results to the online conformal setting, propose several refinements in settings where additional structure is available, and demonstrate its effectiveness through experiments.