# On the Expected Size of Conformal Prediction Sets

arXiv: https://arxiv.org/abs/2306.07254 · HTML: https://mlsanity.com/paper/2306.07254/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 52 references that are in the map.
- First posted on arXiv 12 Jun 2023.

## Builds on (most cited first, 22 of 22)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [Consistent Accelerated Inference via Confident Adaptive Transformers](https://mlsanity.com/paper/2104.08803/) (2021)
- [Fair Conformal Predictors for Applications in Medical Imaging](https://mlsanity.com/paper/2109.04392/) (2021)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Few-shot Conformal Prediction with Auxiliary Tasks](https://mlsanity.com/paper/2102.08898/) (2021)
- [Adaptive Conformal Prediction for Motion Planning among Dynamic Agents](https://mlsanity.com/paper/2212.00278/) (2022)
- [Criteria of efficiency for conformal prediction](https://mlsanity.com/paper/1603.04416/) (2016)
- [Optimized conformal classification using gradient descent approximation](https://mlsanity.com/paper/2105.11255/) (2021)
- [Distribution-Free Federated Learning with Conformal Predictions](https://mlsanity.com/paper/2110.07661/) (2021)
- [From conformal to probabilistic prediction](https://mlsanity.com/paper/1406.5600/) (2014)

## Built on by (most cited first, 13 of 13)

- [Forking Uncertainties: Reliable Prediction and Model Predictive Control with Sequence Models via Conformal Risk Control](https://mlsanity.com/paper/2310.10299/) (2023)
- [Backward Conformal Prediction](https://mlsanity.com/paper/2505.13732/) (2025)
- [Generalization and Informativeness of Conformal Prediction](https://mlsanity.com/paper/2401.11810/) (2024)
- [Conformal Information Pursuit for Interactively Guiding Large Language Models](https://mlsanity.com/paper/2507.03279/) (2025)
- [On the Temperature of Bayesian Graph Neural Networks for Conformal Prediction](https://mlsanity.com/paper/2310.11479/) (2023)
- [Generalization and Informativeness of Weighted Conformal Risk Control Under Covariate Shift](https://mlsanity.com/paper/2501.11413/) (2025)
- [Non-Asymptotic Analysis of Efficiency in Conformalized Regression](https://mlsanity.com/paper/2510.07093/) (2025)
- [Data-Adaptive Tradeoffs among Multiple Risks in Distribution-Free Prediction](https://mlsanity.com/paper/2403.19605/) (2024)
- [On Optimal Data Splitting for Split Conformal Prediction](https://mlsanity.com/paper/2606.31600/) (2026)
- [Quantifying and Improving Adaptivity in Conformal Prediction through Input Transformations](https://mlsanity.com/paper/2511.11472/) (2025)
- [Uncertainty-Aware Transformers: Conformal Prediction for Language Models](https://mlsanity.com/paper/2604.08885/) (2026)
- [Decoupled Conformal Optimisation: Efficient Prediction Sets via Independent Tuning and Calibration](https://mlsanity.com/paper/2605.18354/) (2026)
- [Robust Bayes-Assisted Conformal Prediction](https://mlsanity.com/paper/2607.04236/) (2026)

## Abstract (arXiv)

While conformal predictors reap the benefits of rigorous statistical guarantees on their error frequency, the size of their corresponding prediction sets is critical to their practical utility. Unfortunately, there is currently a lack of finite-sample analysis and guarantees for their prediction set sizes. To address this shortfall, we theoretically quantify the expected size of the prediction sets under the split conformal prediction framework. As this precise formulation cannot usually be calculated directly, we further derive point estimates and high-probability interval bounds that can be empirically computed, providing a practical method for characterizing the expected set size. We corroborate the efficacy of our results with experiments on real-world datasets for both regression and classification problems.