On Optimal Data Splitting for Split Conformal Prediction

2026-06-30

AI Summary

This study addresses the optimal split between training and calibration sets in split conformal prediction, aiming to simultaneously guarantee valid coverage probability and minimize prediction interval length under finite-sample settings. For the first time, we derive analytically the optimal split proportion that minimizes interval length in a general regression framework, and elucidate how factors such as model complexity influence this proportion. Combining theoretical analysis with a data-driven strategy, our approach is applicable across diverse models, including linear regression, nonparametric regression, and neural networks. Experimental results on both synthetic and real-world datasets demonstrate that the proposed splitting strategy substantially shortens prediction intervals while rigorously maintaining the prescribed coverage guarantees.

Abstract

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.

Problem

• split conformal prediction
• data splitting
• prediction interval
• coverage guarantee
• statistical efficiency

Innovation

• optimal data splitting
• split conformal prediction
• prediction interval length
• coverage guarantee
• regression models