Accelerating Conformal Prediction via Approximate Leave-One-Out

2026-06-30

AI Summary

This work addresses the high computational cost of traditional conformal prediction, which requires refitting the model via leave-one-out (LOO) for every sample. We introduce, for the first time, approximate leave-one-out (ALO) from high-dimensional statistics into conformal prediction, constructing an efficient estimator of LOO residuals tailored to a new test point \(x_{n+1}\). This approach avoids repeated model retraining while substantially reducing computational overhead. Theoretical analysis demonstrates that the proposed method asymptotically preserves the coverage and predictive efficiency of exact LOO. Extensive experiments across diverse simulation settings confirm that it achieves comparable statistical performance with dramatically reduced runtime. Our study establishes a scalable, theoretically grounded, and practically viable paradigm for conformal prediction.

Abstract

While conformal prediction provides a general framework for uncertainty quantification in predictive inference, its application is often limited by computational cost. Recent methods, including Jackknife+ and Jackknife-minmax, achieve faster computation by trading a slight loss of efficiency relative to full conformal prediction, but still requires computing leave-one-out refits for all observations. In this paper, we further accelerate conformal prediction by incorporating approximate leave-one-out (ALO) estimators, and establish asymptotic coverage and efficiency. While our proof draws on methods developed for analyzing the consistency of ALO cross-validation risk estimators in high-dimensional statistics, it requires adaptations to handle conformal prediction, where leave-$i$-out residuals are needed for predictions at $x_{n+1}$ rather than just at the training covariate $x_i$. Simulation results validate our theoretical findings, showing that the ALO-based methods achieve coverage and efficiency comparable to the exact methods, while significantly reducing the runtime.

Problem

• conformal prediction
• computational cost
• leave-one-out
• uncertainty quantification
• approximate leave-one-out

Innovation

• conformal prediction
• approximate leave-one-out
• computational efficiency
• uncertainty quantification
• asymptotic coverage