Building Conformal Prediction Intervals with Approximate Message Passing
Lucas Clarté, Lenka Zdeborová
TL;DR
The paper tackles distribution-free uncertainty quantification for regression by accelerating full conformal prediction (FCP) in high dimensions with Approximate Message Passing (AMP). It introduces Taylor-AMP to further speed up computations and proves asymptotic exactness of AMP-based conformal intervals in Gaussian high-dimensional settings, while validating performance on synthetic and real data. The results show that AMP-based intervals closely match exact leave-one-out conformal predictions but with massive speedups, enabling scalable uncertainty quantification for large $n$ and $d$. By bridging conformal prediction with high-dimensional inference, the work provides a practical framework for benchmarking and theoretical exploration of conformal methods in the high-dimensional regime.
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.