Approximating full conformal prediction: distribution free guarantees via the tournament correction

2026-05-27

AI Summary

Full conformal prediction offers rigorous coverage guarantees but suffers from prohibitive computational costs, while existing approximate methods lack distribution-free theoretical assurances. This work proposes a novel approximation framework based on a “tournament” mechanism that, for the first time, achieves strict marginal coverage guarantees without retraining the model for every candidate response value. Under general conditions, the method attains $1 - 2\alpha$ coverage, and under a model stability assumption, it approaches the optimal $1 - \alpha$ coverage. The approach is compatible with existing approximation strategies, substantially reduces computational overhead, and demonstrates superior performance over current approximations both in theoretical guarantees and empirical predictive accuracy.

Abstract

Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split conformal prediction (also called transductive and inductive). Full conformal prediction is widely considered to be statistically more efficient (since split conformal prediction requires data splitting, and therefore can lead to wider prediction intervals due to the resulting loss in sample size), but its implementation is computationally prohibitive, as it requires the underlying model to be refit for every candidate value in the response space. Existing computational shortcuts, such as using a discrete grid of values to approximate the full conformal prediction construction, frequently lack theoretical guarantees on marginal coverage and can fail in practice. To address this limitation, we introduce a novel class of approximations to the full conformal prediction method, based on the idea of \emph{tournaments}, which enables the construction of prediction sets with a rigorous marginal coverage guarantee of $1-2α$. Under stability conditions, the theoretical coverage guarantee tightens to approximately $1-α$. This new framework generalizes the existing method of leave-one-out cross-conformal prediction, while allowing for flexible use of various existing approximation strategies.

Problem

• conformal prediction
• full conformal prediction
• distribution-free guarantees
• computational efficiency
• marginal coverage

Innovation

• conformal prediction
• tournament correction
• distribution-free coverage
• computational approximation
• marginal coverage guarantee