Approximate full conformal prediction in an RKHS

TL;DR

This paper introduces an efficient approximation method for full conformal prediction regions in RKHS, providing theoretical bounds on the approximation's tightness based on smoothness assumptions.

Contribution

It proposes a generic strategy to approximate full conformal prediction regions efficiently and introduces a new measure called thickness to quantify approximation accuracy.

Findings

The approximation is computationally feasible for complex estimators.

Theoretical bounds relate approximation tightness to smoothness conditions.

The method maintains valid coverage properties.

Abstract

Full conformal prediction is a framework that implicitly formulates distribution-free confidence prediction regions for a wide range of estimators. However, a classical limitation of the full conformal framework is the computation of the confidence prediction regions, which is usually impossible since it requires training infinitely many estimators (for real-valued prediction for instance). The main purpose of the present work is to describe a generic strategy for designing a tight approximation to the full conformal prediction region that can be efficiently computed. Along with this approximate confidence region, a theoretical quantification of the tightness of this approximation is developed, depending on the smoothness assumptions on the loss and score functions. The new notion of thickness is introduced for quantifying the discrepancy between the approximate confidence region and the full conformal one.