# On Optimal Data Splitting for Split Conformal Prediction

arXiv: https://arxiv.org/abs/2606.31600 · HTML: https://mlsanity.com/paper/2606.31600/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 47 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 26 of 26)

- [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)
- [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)
- [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)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Class-Conditional Conformal Prediction with Many Classes](https://mlsanity.com/paper/2306.09335/) (2023)
- [Large language model validity via enhanced conformal prediction methods](https://mlsanity.com/paper/2406.09714/) (2024)
- [Fair Conformal Predictors for Applications in Medical Imaging](https://mlsanity.com/paper/2109.04392/) (2021)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [Improving Conditional Coverage via Orthogonal Quantile Regression](https://mlsanity.com/paper/2106.00394/) (2021)
- [Sample-Efficient Safety Assurances using Conformal Prediction](https://mlsanity.com/paper/2109.14082/) (2021)
- [Length Optimization in Conformal Prediction](https://mlsanity.com/paper/2406.18814/) (2024)
- [Criteria of efficiency for conformal prediction](https://mlsanity.com/paper/1603.04416/) (2016)
- [Boosted Conformal Prediction Intervals](https://mlsanity.com/paper/2406.07449/) (2024)
- [Efficient and Differentiable Conformal Prediction with General Function Classes](https://mlsanity.com/paper/2202.11091/) (2022)
- [On the Expected Size of Conformal Prediction Sets](https://mlsanity.com/paper/2306.07254/) (2023)
- [Group-Conditional Conformal Prediction via Quantile Regression Calibration for Crop and Weed Classification](https://mlsanity.com/paper/2308.15094/) (2023)
- [Extreme Conformal Prediction: Reliable Intervals for High-Impact Events](https://mlsanity.com/paper/2505.08578/) (2025)
- [Conformal Prediction Beyond the Horizon: Distribution-Free Inference for Policy Evaluation](https://mlsanity.com/paper/2510.26026/) (2025)

## Built on by (most cited first, 1 of 1)

- [Conformal Prediction and Conditional Coverage for Tabular Foundation Models](https://mlsanity.com/paper/2609.34887/) (2026)

## Abstract (arXiv)

Conformal prediction and its variants, including the split conformal prediction, provide a distribution-free framework for uncertainty quantification by constructing prediction intervals or sets with finite-sample coverage guarantees. The statistical efficiency of these intervals depends critically on how the data are split into training and calibration samples. Despite its practical importance, a principled characterization of the training-calibration split that minimizes prediction interval length while maintaining coverage has remained largely unresolved. In this paper, we develop a theoretical framework for optimal data splitting in split conformal prediction. We first analyze the problem in a general setting and derive analytical characterizations of the length-optimal split ratio under both symmetric and asymmetric regimes. We then show how the general results specialize to several commonly used regression settings, including linear regression, nonparametric regression, and neural networks, thereby demonstrating the scope of the framework. We also describe a data-based method for selecting the optimal proportion. Our analysis clarifies how model-related features govern the optimal allocation of samples between training and calibration and provides principled guidance for constructing shorter prediction intervals. Experiments on both synthetic and real-world datasets demonstrate the applicability of the proposed methodology across a variety of practical scenarios.