# Prediction Sets Adaptive to Unknown Covariate Shift

arXiv: https://arxiv.org/abs/2203.06126 · HTML: https://mlsanity.com/paper/2203.06126/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 47 references that are in the map.
- First posted on arXiv 11 Mar 2022.

## Builds on (most cited first, 8 of 8)

- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Universal sieve-based strategies for efficient estimation using machine learning tools](https://mlsanity.com/paper/2003.01856/) (2020)

## Built on by (most cited first, 22 of 22)

- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [PAC Prediction Sets Under Label Shift](https://mlsanity.com/paper/2310.12964/) (2023)
- [Prompt Risk Control: A Rigorous Framework for Responsible Deployment of Large Language Models](https://mlsanity.com/paper/2311.13628/) (2023)
- [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)
- [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)
- [SymmPI: Predictive Inference for Data with Group Symmetries](https://mlsanity.com/paper/2312.16160/) (2023)
- [Conformal Information Pursuit for Interactively Guiding Large Language Models](https://mlsanity.com/paper/2507.03279/) (2025)
- [Efficient and Multiply Robust Risk Estimation under General Forms of Dataset Shift](https://mlsanity.com/paper/2306.16406/) (2023)
- [Non-exchangeable Conformal Prediction with Optimal Transport: Tackling Distribution Shifts with Unlabeled Data](https://mlsanity.com/paper/2507.10425/) (2025)
- [Statistical Methods in Generative AI](https://mlsanity.com/paper/2509.07054/) (2025)
- [Distributionally robust risk evaluation with an isotonic constraint](https://mlsanity.com/paper/2407.06867/) (2024)
- [Singleton-Optimized Conformal Prediction](https://mlsanity.com/paper/2509.24095/) (2025)
- [Conformal Prediction Beyond the Horizon: Distribution-Free Inference for Policy Evaluation](https://mlsanity.com/paper/2510.26026/) (2025)
- [A Conditional Distribution Equality Testing Framework using Deep Generative Learning](https://mlsanity.com/paper/2509.17729/) (2025)
- [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)
- [Distribution-Free Predictive Inference under Unknown Temporal Drift](https://mlsanity.com/paper/2406.06516/) (2024)
- [MoRF-AST: Calibrated Probabilistic Virtual Sensing for Structural Monitoring under Changing Operating Conditions](https://mlsanity.com/paper/2608.24531/) (2026)
- [GeoDose-CP: Graph-Local Conformal Inference for Continuous-Treatment Earth Observation](https://mlsanity.com/paper/2609.28895/) (2026)

## Abstract (arXiv)

Predicting sets of outcomes -- instead of unique outcomes -- is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to unknown covariate shift -- a prevalent issue in practice -- poses a serious unsolved challenge. In this paper, we show that prediction sets with finite-sample coverage guarantee are uninformative and propose a novel flexible distribution-free method, PredSet-1Step, to efficiently construct prediction sets with an asymptotic coverage guarantee under unknown covariate shift. We formally show that our method is textitasymptotically probably approximately correct, having well-calibrated coverage error with high confidence for large samples. We illustrate that it achieves nominal coverage in a number of experiments and a data set concerning HIV risk prediction in a South African cohort study. Our theory hinges on a new bound for the convergence rate of the coverage of Wald confidence intervals based on general asymptotically linear estimators.