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

arXiv cs.AI / 3/30/2026

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Key Points

The paper introduces KMM-CP, a conformal prediction framework that uses Kernel Mean Matching to correct for covariate shift and maintain uncertainty quantification quality under violated exchangeability assumptions.
It argues that KMM can directly manage the bias–variance drivers of conformal coverage error by minimizing RKHS moment discrepancy under explicit weight constraints.
The authors provide asymptotic coverage guarantees under mild conditions and introduce a selective variant that limits correction to regions with reliable support overlap to improve stability.
Experiments on molecular property prediction benchmarks under realistic distribution shifts show KMM-CP reduces the coverage gap by more than 50% versus existing methods, and the code is publicly available.

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.