Building Conformal Prediction Intervals with Approximate Message Passing

TL;DR

This paper introduces a fast AMP-based algorithm for conformal prediction intervals in high-dimensional generalized linear regression, achieving near-baseline accuracy with significantly reduced computation.

Contribution

It develops a novel AMP-based method to efficiently approximate conformity scores for conformal prediction in high dimensions, bridging uncertainty quantification and large-scale problems.

Findings

Produces prediction intervals close to baseline methods

Achieves orders of magnitude faster computation

Conformity scores converge to exact values in high dimensions

Abstract

Conformal prediction has emerged as a powerful tool for building prediction intervals that are valid in a distribution-free way. However, its evaluation may be computationally costly, especially in the high-dimensional setting where the dimensionality and sample sizes are both large and of comparable magnitudes. To address this challenge in the context of generalized linear regression, we propose a novel algorithm based on Approximate Message Passing (AMP) to accelerate the computation of prediction intervals using full conformal prediction, by approximating the computation of conformity scores. Our work bridges a gap between modern uncertainty quantification techniques and tools for high-dimensional problems involving the AMP algorithm. We evaluate our method on both synthetic and real data, and show that it produces prediction intervals that are close to the baseline methods, while being orders of magnitude faster. Additionally, in the high-dimensional limit and under assumptions on the data distribution, the conformity scores computed by AMP converge to the one computed exactly, which allows theoretical study and benchmarking of conformal methods in high dimensions.