Conformal Prediction for Molecular Properties under Label Shift

Conformal prediction provides distribution-free uncertainty quantification under exchangeability. However, this assumption is violated by label shift, where the marginal distribution of labels changes while the conditional distribution of inputs given labels remains stable. Under such shifts, standard conformal procedures no longer maintain their intended coverage behavior. Existing approaches address this via importance weighting. They pair the reweighting with residual-based nonconformity scores that ignore predictive uncertainty. The resulting intervals have uniform width. Bayesian conformal methods produce adaptive intervals by leveraging predictive distributions. They evaluate conformity under the source predictive, which is misaligned with the target domain under label shift. We propose the Label-Shift-Adjusted Bayesian Score (LSA score), a nonconformity score derived from a posterior predictive tilting identity. This identity shows that the target predictive is an importance-weighted transformation of the source predictive. We use it to derive a direct correction to the Bayesian score. We evaluate the method on molecular property prediction under controlled label shift. The LSA score consistently yields shorter intervals than residual-based and source-based Bayesian scores. Coverage in the target domain remains comparable. Under stronger shift, all methods incur some coverage loss due to pseudo-label-based density-ratio estimation. The LSA score is defined for any source predictive with a tractable log-density. We instantiate it with Bayesian Ridge Regression, where the correction admits a closed form.

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.

We consider the problem of uncertainty quantification for a pretrained classification model deployed under unknown distribution shift. We propose Audited Conformal Prediction (ACP), a method that leverages a small labeled dataset from the target population to train an auxiliary audit model identifying inputs where the legacy model is likely to fail. By integrating the audit model's outputs into the conformal prediction framework, ACP produces prediction sets that guarantee marginal coverage while achieving substantially higher conditional coverage in practice than existing approaches. We develop and analyze two complementary integration strategies -- one targeting marginal coverage with improved conditional performance, the other providing explicit group-conditional coverage guarantees -- and establish theoretical guarantees for both. Experiments on synthetic and real-world datasets validate the method and illustrate trade-offs between prediction set size and conditional coverage.