Efficient and Differentiable Conformal Prediction with General Function Classes

TL;DR

This paper introduces a generalized conformal prediction framework that optimizes prediction set efficiency using multiple learnable parameters and a gradient-based algorithm, achieving valid coverage and improved efficiency.

Contribution

It extends conformal prediction to multiple parameters, enabling more efficient prediction sets while maintaining valid coverage, through a novel gradient-based optimization approach.

Findings

Achieves approximate valid coverage in various applications.

Significantly improves prediction set efficiency over existing methods.

Demonstrates effectiveness in prediction intervals, multi-output regression, and image classification.

Abstract

Quantifying the data uncertainty in learning tasks is often done by learning a prediction interval or prediction set of the label given the input. Two commonly desired properties for learned prediction sets are \emph{valid coverage} and \emph{good efficiency} (such as low length or low cardinality). Conformal prediction is a powerful technique for learning prediction sets with valid coverage, yet by default its conformalization step only learns a single parameter, and does not optimize the efficiency over more expressive function classes. In this paper, we propose a generalization of conformal prediction to multiple learnable parameters, by considering the constrained empirical risk minimization (ERM) problem of finding the most efficient prediction set subject to valid empirical coverage. This meta-algorithm generalizes existing conformal prediction algorithms, and we show that it achieves approximate valid population coverage and near-optimal efficiency within class, whenever the function class in the conformalization step is low-capacity in a certain sense. Next, this ERM problem is challenging to optimize as it involves a non-differentiable coverage constraint. We develop a gradient-based algorithm for it by approximating the original constrained ERM using differentiable surrogate losses and Lagrangians. Experiments show that our algorithm is able to learn valid prediction sets and improve the efficiency significantly over existing approaches in several applications such as prediction intervals with improved length, minimum-volume prediction sets for multi-output regression, and label prediction sets for image classification.