# Universal distribution of the empirical coverage in split conformal prediction

arXiv: https://arxiv.org/abs/2303.02770 · HTML: https://mlsanity.com/paper/2303.02770/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 11 references that are in the map.
- First posted on arXiv 5 Mar 2023.

## Builds on (most cited first, 4 of 4)

- [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: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Distribution-Free Finite-Sample Guarantees and Split Conformal Prediction](https://mlsanity.com/paper/2210.14735/) (2022)

## Built on by (most cited first, 15 of 15)

- [Transductive conformal inference with adaptive scores](https://mlsanity.com/paper/2310.18108/) (2023)
- [Anytime-Valid Conformal Risk Control](https://mlsanity.com/paper/2602.04364/) (2026)
- [Conformal prediction for frequency-severity modeling](https://mlsanity.com/paper/2307.13124/) (2023)
- [Transductive Conformal Inference for Full Ranking](https://mlsanity.com/paper/2501.11384/) (2025)
- [Stacked conformal prediction](https://mlsanity.com/paper/2505.12578/) (2025)
- [Fundamental bounds on efficiency-confidence trade-off for transductive conformal prediction](https://mlsanity.com/paper/2509.04631/) (2025)
- [Probabilistic Conformal Coverage Guarantees in Small-Data Settings](https://mlsanity.com/paper/2509.15349/) (2025)
- [Conformal Prediction via Transported Beta Laws](https://mlsanity.com/paper/2605.19024/) (2026)
- [Projected random forests and conformal prediction of circular data](https://mlsanity.com/paper/2410.24145/) (2024)
- [Class conditional conformal prediction for multiple inputs by p-value aggregation](https://mlsanity.com/paper/2507.07150/) (2025)
- [Conformal Tradeoffs: Operational Profiles Beyond Coverage](https://mlsanity.com/paper/2602.18045/) (2026)
- [Skew-adaptive conformal prediction](https://mlsanity.com/paper/2605.16145/) (2026)
- [Everywhere Valid Bounds on False Discovery Proportions in Conformal Inference](https://mlsanity.com/paper/2605.20726/) (2026)
- [Certified Against Which Oracle? Execution Labels Set the Reported Risk of Conformal Abstention for Text-to-SQL](https://mlsanity.com/paper/2609.25938/) (2026)
- [Scaling Full Conformal Image Classifiers](https://mlsanity.com/paper/2609.37298/) (2026)

## Abstract (arXiv)

When split conformal prediction operates in batch mode with exchangeable data, we determine the exact distribution of the empirical coverage of prediction sets produced for a finite batch of future observables, as well as the exact distribution of its almost sure limit when the batch size goes to infinity. Both distributions are universal, being determined solely by the nominal miscoverage level and the calibration sample size, thereby establishing a criterion for choosing the minimum required calibration sample size in applications.