# Set-Preserving Calibration from Conformal P-Values to E-Values

arXiv: https://arxiv.org/abs/2606.03600 · HTML: https://mlsanity.com/paper/2606.03600/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 20 of 20)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Selection and Aggregation of Conformal Prediction Sets](https://mlsanity.com/paper/2104.13871/) (2021)
- [Merging uncertainty sets via majority vote](https://mlsanity.com/paper/2401.09379/) (2024)
- [E-Values Expand the Scope of Conformal Prediction](https://mlsanity.com/paper/2503.13050/) (2025)
- [Conformal e-prediction](https://mlsanity.com/paper/2001.05989/) (2020)
- [Multi Split Conformal Prediction](https://mlsanity.com/paper/2103.00627/) (2021)
- [Enhancing Conformal Prediction Using E-Test Statistics](https://mlsanity.com/paper/2403.19082/) (2024)
- [Martingale Methods for Sequential Estimation of Convex Functionals and Divergences](https://mlsanity.com/paper/2103.09267/) (2021)
- [Randomized and Exchangeable Improvements of Markov's, Chebyshev's and Chernoff's Inequalities](https://mlsanity.com/paper/2304.02611/) (2023)
- [Backward Conformal Prediction](https://mlsanity.com/paper/2505.13732/) (2025)
- [Measuring Evidence against Exchangeability and Group Invariance with E-values](https://mlsanity.com/paper/2310.01153/) (2023)
- [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)
- [Symmetric Aggregation of Conformity Scores for Efficient Uncertainty Sets](https://mlsanity.com/paper/2512.06945/) (2025)
- [Post-hoc α Hypothesis Testing and the Post-hoc p-value](https://mlsanity.com/paper/2312.08040/) (2023)

## Abstract (arXiv)

Standard conformal prediction (CP) procedures are typically formulated in terms of p-values, but reliance on p-values alone limits flexibility, for example, when combining dependent evidence across models or data splits. Recent work has explored e-value formulations for conformal inference, yet a direct connection between p- and e-value formulations in CP has been missing, especially regarding their statistical efficiency. We first identify limitations of classical p-to-e calibrators in the CP setting, showing that they are not set-preserving and can lead to overly conservative prediction sets. To address this, we propose a novel P2E calibrator that converts conformal p-values into e-values without altering the prediction set induced by the original conformal p-value. We establish both theoretically and empirically that our calibrator can yield significant efficiency gains over existing p-to-e calibrators. This e-value formulation enables principled use of recent advances in e-value merging and randomization, where we demonstrate its impact in two applications: cross-conformal prediction (CCP), whose variants typically provide only approximate 1-2α coverage, and conformal aggregation (CA). In both cases, our e-value-based methods satisfy the desired 1-α coverage guarantee while improving efficiency over standard baselines. More broadly, our approach expands the flexibility of CP and opens new directions for efficient, distribution-free uncertainty quantification.