# Accelerating Conformal Prediction via Approximate Leave-One-Out

arXiv: https://arxiv.org/abs/2606.31915 · HTML: https://mlsanity.com/paper/2606.31915/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 24 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 13 of 13)

- [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)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Computing Full Conformal Prediction Set with Approximate Homotopy](https://mlsanity.com/paper/1909.09365/) (2019)
- [Consistent Risk Estimation in Moderately High-Dimensional Linear Regression](https://mlsanity.com/paper/1902.01753/) (2019)
- [On Optimal Generalizability in Parametric Learning](https://mlsanity.com/paper/1711.05323/) (2017)
- [Error bounds in estimating the out-of-sample prediction error using leave-one-out cross validation in high-dimensions](https://mlsanity.com/paper/2003.01770/) (2020)
- [Approximating Full Conformal Prediction at Scale via Influence Functions](https://mlsanity.com/paper/2202.01315/) (2022)
- [Approximate Leave-One-Out for High-Dimensional Non-Differentiable Learning Problems](https://mlsanity.com/paper/1810.02716/) (2018)
- [Theoretical Analysis of Leave-one-out Cross Validation for Non-differentiable Penalties under High-dimensional Settings](https://mlsanity.com/paper/2402.08543/) (2024)
- [Approximate Leave-one-out Cross Validation for Regression with ℓ1 Regularizers (extended version)](https://mlsanity.com/paper/2310.17629/) (2023)
- [Building Conformal Prediction Intervals with Approximate Message Passing](https://mlsanity.com/paper/2410.16493/) (2024)
- [Stability of a Generalized Debiased Lasso with Applications to Resampling-Based Variable Selection](https://mlsanity.com/paper/2405.03063/) (2024)

## Abstract (arXiv)

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 xn+1 rather than just at the training covariate xi. 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.