# Generalization and Informativeness of Weighted Conformal Risk Control Under Covariate Shift

arXiv: https://arxiv.org/abs/2501.11413 · HTML: https://mlsanity.com/paper/2501.11413/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 20 Jan 2025.

## Builds on (most cited first, 12 of 12)

- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [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)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Fair Conformal Predictors for Applications in Medical Imaging](https://mlsanity.com/paper/2109.04392/) (2021)
- [Provably Robust Conformal Prediction with Improved Efficiency](https://mlsanity.com/paper/2404.19651/) (2024)
- [Forking Uncertainties: Reliable Prediction and Model Predictive Control with Sequence Models via Conformal Risk Control](https://mlsanity.com/paper/2310.10299/) (2023)
- [Robust Yet Efficient Conformal Prediction Sets](https://mlsanity.com/paper/2407.09165/) (2024)
- [On the Expected Size of Conformal Prediction Sets](https://mlsanity.com/paper/2306.07254/) (2023)
- [Generalization and Informativeness of Conformal Prediction](https://mlsanity.com/paper/2401.11810/) (2024)
- [Base Station ON-OFF Switching in 5G Wireless Networks: Approaches and Challenges](https://mlsanity.com/paper/1703.09875/) (2017)

## Built on by (most cited first, 3 of 3)

- [A Joint Finite-Sample Certificate for Adaptive Selective Conformal Risk Control](https://mlsanity.com/paper/2606.08517/) (2026)
- [Uncertainty Quantification and Data Efficiency in AI: An Information-Theoretic Perspective](https://mlsanity.com/paper/2512.05267/) (2025)
- [Weighted Bayesian Conformal Prediction](https://mlsanity.com/paper/2604.06464/) (2026)

## Abstract (arXiv)

Predictive models are often required to produce reliable predictions under statistical conditions that are not matched to the training data. A common type of training-testing mismatch is covariate shift, where the conditional distribution of the target variable given the input features remains fixed, while the marginal distribution of the inputs changes. Weighted conformal risk control (W-CRC) uses data collected during the training phase to convert point predictions into prediction sets with valid risk guarantees at test time despite the presence of a covariate shift. However, while W-CRC provides statistical reliability, its efficiency -- measured by the size of the prediction sets -- can only be assessed at test time. In this work, we relate the generalization properties of the base predictor to the efficiency of W-CRC under covariate shifts. Specifically, we derive a bound on the inefficiency of the W-CRC predictor that depends on algorithmic hyperparameters and task-specific quantities available at training time. This bound offers insights on relationships between the informativeness of the prediction sets, the extent of the covariate shift, and the size of the calibration and training sets. Experiments on fingerprinting-based localization validate the theoretical results.