# Coverage Guarantees for Pseudo-Calibrated Conformal Prediction under Distribution Shift

arXiv: https://arxiv.org/abs/2602.14913 · HTML: https://mlsanity.com/paper/2602.14913/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 26 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Builds on (most cited first, 22 of 22)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Understanding Self-Training for Gradual Domain Adaptation](https://mlsanity.com/paper/2002.11361/) (2020)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [Calibrated Prediction with Covariate Shift via Unsupervised Domain Adaptation](https://mlsanity.com/paper/2003.00343/) (2020)
- [Doubly Robust Calibration of Prediction Sets under Covariate Shift](https://mlsanity.com/paper/2203.01761/) (2022)
- [Gradual Domain Adaptation: Theory and Algorithms](https://mlsanity.com/paper/2310.13852/) (2023)
- [Wasserstein-regularized Conformal Prediction under General Distribution Shift](https://mlsanity.com/paper/2501.13430/) (2025)
- [Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations](https://mlsanity.com/paper/2502.14105/) (2025)
- [Probably Approximately Correct Labels](https://mlsanity.com/paper/2506.10908/) (2025)
- [Mirror Online Conformal Prediction with Intermittent Feedback](https://mlsanity.com/paper/2503.10345/) (2025)
- [Adapting Prediction Sets to Distribution Shifts Without Labels](https://mlsanity.com/paper/2406.01416/) (2024)
- [WQLCP: Weighted Adaptive Conformal Prediction for Robust Uncertainty Quantification Under Distribution Shifts](https://mlsanity.com/paper/2505.19587/) (2025)
- [Non-exchangeable Conformal Prediction with Optimal Transport: Tackling Distribution Shifts with Unlabeled Data](https://mlsanity.com/paper/2507.10425/) (2025)
- [Learning minimal volume uncertainty ellipsoids](https://mlsanity.com/paper/2405.02441/) (2024)
- [Multiply Robust Conformal Risk Control with Coarsened Data](https://mlsanity.com/paper/2508.15489/) (2025)
- [Optimizing In-Context Learning for Efficient Full Conformal Prediction](https://mlsanity.com/paper/2509.01840/) (2025)

## Built on by (most cited first, 1 of 1)

- [The Label Complexity of Useful Class-Conditional Prediction Sets under Distribution Shift](https://mlsanity.com/paper/2607.18088/) (2026)

## Abstract (arXiv)

Conformal prediction (CP) offers distribution-free marginal coverage guarantees under an exchangeability assumption, but these guarantees can fail if the data distribution shifts. We analyze the use of pseudo-calibration as a tool to counter this performance loss under a bounded label-conditional covariate shift model. Using tools from domain adaptation, we derive a lower bound on target coverage in terms of the source-domain loss of the classifier and a Wasserstein measure of the shift. Using this result, we provide a method to design pseudo-calibrated sets that inflate the conformal threshold by a slack parameter to keep target coverage above a prescribed level. Finally, we propose a source-tuned pseudo-calibration algorithm that interpolates between hard pseudo-labels and randomized labels as a function of classifier uncertainty. Numerical experiments show that our bounds qualitatively track pseudo-calibration behavior and that the source-tuned scheme mitigates coverage degradation under distribution shift while maintaining nontrivial prediction set sizes.