Building Conformal Prediction Intervals with Approximate Message Passing
This addresses efficiency issues for researchers and practitioners using conformal prediction in high-dimensional settings, representing an incremental improvement by bridging uncertainty quantification with high-dimensional tools.
The paper tackles the computational cost of conformal prediction in high-dimensional generalized linear regression by proposing an Approximate Message Passing (AMP)-based algorithm to approximate conformity scores, resulting in prediction intervals close to baseline methods but orders of magnitude faster.
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.