KMM-CP: Practical Conformal Prediction under Covariate Shift via Selective Kernel Mean Matching

2026-03-27

AI Summary

This work addresses the challenge of conformal prediction under covariate shift, where limited overlap between training and test distribution supports leads to unstable importance weighting and coverage failure. To mitigate this, the authors propose the KMM-CP framework, which leverages kernel mean matching (KMM) in a reproducing kernel Hilbert space (RKHS) to minimize distributional moment discrepancies and correct for shift. Crucially, they introduce a selective mechanism that applies correction only within reliably overlapping regions of the support, thereby enhancing coverage stability. Evaluated on molecular property prediction benchmarks, the method reduces coverage gaps by over 50% compared to existing approaches, demonstrating superior robustness and effectiveness under realistic distributional shifts.

Abstract

Uncertainty quantification is essential for deploying machine learning models in high-stakes domains such as scientific discovery and healthcare. Conformal Prediction (CP) provides finite-sample coverage guarantees under exchangeability, an assumption often violated in practice due to distribution shift. Under covariate shift, restoring validity requires importance weighting, yet accurate density-ratio estimation becomes unstable when training and test distributions exhibit limited support overlap. We propose KMM-CP, a conformal prediction framework based on Kernel Mean Matching (KMM) for covariate-shift correction. We show that KMM directly controls the bias-variance components governing conformal coverage error by minimizing RKHS moment discrepancy under explicit weight constraints, and establish asymptotic coverage guarantees under mild conditions. We then introduce a selective extension that identifies regions of reliable support overlap and restricts conformal correction to this subset, further improving stability in low-overlap regimes. Experiments on molecular property prediction benchmarks with realistic distribution shifts show that KMM-CP reduces coverage gap by over 50% compared to existing approaches. The code is available at https://github.com/siddharthal/KMM-CP.

Problem

• Conformal Prediction
• Covariate Shift
• Uncertainty Quantification
• Distribution Shift
• Importance Weighting

Innovation

• Conformal Prediction
• Covariate Shift
• Kernel Mean Matching
• Uncertainty Quantification
• Distribution Shift