Weight Clipping for Robust Conformal Inference under Unbounded Covariate Shifts

2026-05-03

AI Summary

Under unbounded covariate shift, weighted conformal prediction suffers from significant undercoverage due to the high variance and overfitting inherent in density ratio estimation. This work proposes Clipped Least-Squares Importance Fitting (CLISF), a method that reduces the variance of density ratio estimates through bounded importance weights and corrects undercoverage by targeting a slightly inflated coverage level. CLISF provides the first theoretical guarantees for weight clipping in conformal prediction, ensuring dataset-conditional coverage while avoiding sample complexity that explodes with higher-order moments of the true density ratio. Empirical evaluations on both synthetic and real-world benchmarks demonstrate that CLISF effectively mitigates undercoverage and substantially enhances the reliability of prediction sets.

Abstract

Conformal prediction (CP) provides powerful, distribution-free prediction sets, but its guarantees rely on the exchangeability of training and test data, which is often violated in practice due to covariate shifts. While weighted conformal prediction (WCP) is designed to handle such shifts, it can suffer from significant undercoverage when the density ratio between the distributions is unbounded and/or must be learned. This is because of both overfitting in learning the density ratio, and high variance in estimating the nonconformity score threshold. To address this, we introduce clipped least-squares importance fitting (CLISF) as a reduced-variance method for density ratio estimation. Specifically, we show that density ratios learned using CLISF, when plugged into WCP, have bounded expected undercoverage. Furthermore, we show that the undercoverage can be corrected by running WCP with a slightly inflated coverage target; crucially, we are able to estimate the required level of inflation from the data. We provide the first theoretical guarantees for weight clipping in conformal inference, achieving dataset-conditional coverage with a sample complexity that does not blow up with the higher moments of the true density ratio -- a key limitation of prior work. We verify our results on real-world benchmarks and synthetic data.

Problem

• conformal prediction
• covariate shift
• density ratio estimation
• undercoverage
• unbounded shifts

Innovation

• weight clipping
• conformal prediction
• covariate shift
• density ratio estimation
• coverage guarantee