# Doubly Robust Calibration of Prediction Sets under Covariate Shift

arXiv: https://arxiv.org/abs/2203.01761 · HTML: https://mlsanity.com/paper/2203.01761/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2022.

## Built on by (most cited first, 30 of 40)

- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Conformal Validity Guarantees Exist for Any Data Distribution (and How to Find Them)](https://mlsanity.com/paper/2405.06627/) (2024)
- [Conformal Prediction with Temporal Quantile Adjustments](https://mlsanity.com/paper/2205.09940/) (2022)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Conformal Prediction for Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2407.03094/) (2024)
- [WATCH: Adaptive Monitoring for AI Deployments via Weighted-Conformal Martingales](https://mlsanity.com/paper/2505.04608/) (2025)
- [TabPFN: One Model to Rule Them All?](https://mlsanity.com/paper/2505.20003/) (2025)
- [Kandinsky Conformal Prediction: Beyond Class- and Covariate-Conditional Coverage](https://mlsanity.com/paper/2502.17264/) (2025)
- [Error-quantified Conformal Inference for Time Series](https://mlsanity.com/paper/2502.00818/) (2025)
- [Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularization](https://mlsanity.com/paper/2502.13030/) (2025)
- [Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations](https://mlsanity.com/paper/2502.14105/) (2025)
- [Multi-Source Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2405.09331/) (2024)
- [What If We Had Used a Different App? Reliable Counterfactual KPI Analysis in Wireless Systems](https://mlsanity.com/paper/2410.00150/) (2024)
- [Conformal Policy Control](https://mlsanity.com/paper/2603.02196/) (2026)
- [Post-selection Inference for Conformal Prediction: Trading off Coverage for Precision](https://mlsanity.com/paper/2304.06158/) (2023)
- [Efficient and Multiply Robust Risk Estimation under General Forms of Dataset Shift](https://mlsanity.com/paper/2306.16406/) (2023)
- [Conformal Predictive Systems Under Covariate Shift](https://mlsanity.com/paper/2404.15018/) (2024)
- [Non-exchangeable Conformal Prediction with Optimal Transport: Tackling Distribution Shifts with Unlabeled Data](https://mlsanity.com/paper/2507.10425/) (2025)
- [Optimal Aggregation of Prediction Intervals under Unsupervised Domain Shift](https://mlsanity.com/paper/2405.10302/) (2024)
- [Distributionally robust risk evaluation with an isotonic constraint](https://mlsanity.com/paper/2407.06867/) (2024)
- [On the Role of Surrogates in Conformal Inference of Individual Causal Effects](https://mlsanity.com/paper/2412.12365/) (2024)
- [Distribution-informed Online Conformal Prediction](https://mlsanity.com/paper/2512.07770/) (2025)
- [Boosting Test Performance with Importance Sampling--a Subpopulation Perspective](https://mlsanity.com/paper/2412.13003/) (2024)
- [Online conformal inference with retrospective adjustment for faster adaptation to distribution shift](https://mlsanity.com/paper/2511.04275/) (2025)
- [Distribution Shift in Missing Data Imputation: A Risk-Based Perspective and Importance-Weighted Correction under MAR](https://mlsanity.com/paper/2602.06713/) (2026)
- [Coverage Guarantees for Pseudo-Calibrated Conformal Prediction under Distribution Shift](https://mlsanity.com/paper/2602.14913/) (2026)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [Weighted Bayesian Conformal Prediction](https://mlsanity.com/paper/2604.06464/) (2026)
- [Sharp training-conditional coverage for conformal prediction under covariate shift](https://mlsanity.com/paper/2609.33456/) (2026)

## Abstract (arXiv)

Conformal prediction has received tremendous attention in recent years and has offered new solutions to problems in missing data and causal inference; yet these advances have not leveraged modern semiparametric efficiency theory for more robust and efficient uncertainty quantification. In this paper, we consider the problem of obtaining distribution-free prediction regions accounting for a shift in the distribution of the covariates between the training and test data. Under an explainable covariate shift assumption analogous to the standard missing at random assumption, we propose three variants of a general framework to construct well-calibrated prediction regions for the unobserved outcome in the test sample. Our approach is based on the efficient influence function for the quantile of the unobserved outcome in the test population combined with an arbitrary machine learning prediction algorithm, without compromising asymptotic coverage. Next, we extend our approach to account for departure from the explainable covariate shift assumption in a semiparametric sensitivity analysis for potential latent covariate shift. In all cases, we establish that the resulting prediction sets eventually attain nominal average coverage in large samples. This guarantee is a consequence of the product bias form of our proposal which implies correct coverage if either the propensity score or the conditional distribution of the response is estimated sufficiently well. Our results also provide a framework for construction of doubly robust prediction sets of individual treatment effects, under both unconfoundedness and allowing for some degree of unmeasured confounding. Finally, we discuss aggregation of prediction sets from different machine learning algorithms for optimal prediction and illustrate the performance of our methods in both synthetic and real data.