# Improving the statistical efficiency of cross-conformal prediction

arXiv: https://arxiv.org/abs/2503.01495 · HTML: https://mlsanity.com/paper/2503.01495/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 3 Mar 2025.

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

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [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)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [Predictive Inference Is Free with the Jackknife+-after-Bootstrap](https://mlsanity.com/paper/2002.09025/) (2020)
- [Selection and Aggregation of Conformal Prediction Sets](https://mlsanity.com/paper/2104.13871/) (2021)
- [Conformal prediction with local weights: randomization enables local guarantees](https://mlsanity.com/paper/2310.07850/) (2023)
- [Exchangeability, Conformal Prediction, and Rank Tests](https://mlsanity.com/paper/2005.06095/) (2020)
- [Conformal prediction under ambiguous ground truth](https://mlsanity.com/paper/2307.09302/) (2023)
- [Merging uncertainty sets via majority vote](https://mlsanity.com/paper/2401.09379/) (2024)
- [Multi Split Conformal Prediction](https://mlsanity.com/paper/2103.00627/) (2021)
- [Randomized and Exchangeable Improvements of Markov's, Chebyshev's and Chernoff's Inequalities](https://mlsanity.com/paper/2304.02611/) (2023)
- [JAWS: Auditing Predictive Uncertainty Under Covariate Shift](https://mlsanity.com/paper/2207.10716/) (2022)
- [Conformal prediction after data-dependent model selection](https://mlsanity.com/paper/2408.07066/) (2024)
- [Discretized conformal prediction for efficient distribution-free inference](https://mlsanity.com/paper/1709.06233/) (2017)

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

- [Symmetric Aggregation of Conformity Scores for Efficient Uncertainty Sets](https://mlsanity.com/paper/2512.06945/) (2025)
- [Non-Asymptotic Analysis of Efficiency in Conformalized Regression](https://mlsanity.com/paper/2510.07093/) (2025)
- [Co-optimization for Adaptive Conformal Prediction](https://mlsanity.com/paper/2603.01719/) (2026)
- [CAOS: Conformal Aggregation of One-Shot Predictors](https://mlsanity.com/paper/2601.05219/) (2026)
- [Set-Preserving Calibration from Conformal P-Values to E-Values](https://mlsanity.com/paper/2606.03600/) (2026)

## Abstract (arXiv)

Vovk (2015) introduced cross-conformal prediction, a modification of split conformal designed to improve the width of prediction sets. The method, when trained with a miscoverage rate equal to α and n gg K, ensures a marginal coverage of at least 1 - 2α - 2(1-α)(K-1)/(n+K), where n is the number of observations and K denotes the number of folds. A simple modification of the method achieves coverage of at least 1-2α. In this work, we propose new variants of both methods that yield smaller prediction sets without compromising the latter theoretical guarantees. The proposed methods are based on recent results deriving more statistically efficient combination of p-values that leverage exchangeability and randomization. Simulations confirm the theoretical findings and bring out some important tradeoffs.