Jonkers and Ziegel's CPS adapts to distribution shifts via weighted permutations

Jonkers and Ziegel address a critical limitation of conformal predictive systems (CPS): their reliance on exchangeability. In real-world applications—like online learning, active learning, or biomedical trials—data distributions can shift unexpectedly, invalidating standard conformal intervals. Their generalized CPS encodes distributional shifts as observation-specific permutation weights, producing predictive systems that remain valid as long as the test point is, conditionally on the unordered sample, a weighted draw from the observed atoms. Because these weights must often be estimated, they introduce weight-uncertainty boxes that construct robust CPS envelopes with either finite-sample or asymptotic confidence guarantees. Efficient computation is provided for three common CPS variants: conformity-measure CPS, conformal binning, and conformal isotonic distributional regression.

The method is validated on two challenging scenarios: covariate shift in synthetic data and real-world feedback-driven biomolecular design. Under covariate shift, the predictive bands automatically widen when the shift is severe and tighten as more data accumulates. For biomolecular design—where iterative experimental feedback alters the data distribution—the approach delivers calibrated bands that reflect true uncertainty. This work offers a principled framework for reliable uncertainty quantification in non-stationary environments, with potential applications in high-stakes ML deployments where distributional robustness is essential. The paper is available on arXiv (2606.11044).