# Uncertainty Quantification With Multiple Sources

arXiv: https://arxiv.org/abs/2405.06479 · HTML: https://mlsanity.com/paper/2405.06479/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 37 references that are in the map.
- First posted on arXiv 10 May 2024.

## Builds on (most cited first, 18 of 18)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Conformal Prediction Under Feedback Covariate Shift for Biomolecular Design](https://mlsanity.com/paper/2202.03613/) (2022)
- [Conformalized Survival Analysis](https://mlsanity.com/paper/2103.09763/) (2021)
- [Conformal prediction with local weights: randomization enables local guarantees](https://mlsanity.com/paper/2310.07850/) (2023)
- [Distribution-Free Prediction Sets for Two-Layer Hierarchical Models](https://mlsanity.com/paper/1809.07441/) (2018)
- [Merging uncertainty sets via majority vote](https://mlsanity.com/paper/2401.09379/) (2024)
- [Model-free selective inference under covariate shift via weighted conformal p-values](https://mlsanity.com/paper/2307.09291/) (2023)
- [Multi Split Conformal Prediction](https://mlsanity.com/paper/2103.00627/) (2021)
- [Distribution-free inference with hierarchical data](https://mlsanity.com/paper/2306.06342/) (2023)
- [Group-Weighted Conformal Prediction](https://mlsanity.com/paper/2401.17452/) (2024)
- [SymmPI: Predictive Inference for Data with Group Symmetries](https://mlsanity.com/paper/2312.16160/) (2023)
- [Predictive Inference in Multi-environment Scenarios](https://mlsanity.com/paper/2403.16336/) (2024)

## Built on by (most cited first, 2 of 2)

- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Distribution-Free Predictive Inference under Unknown Temporal Drift](https://mlsanity.com/paper/2406.06516/) (2024)

## Abstract (arXiv)

Weighted conformal prediction (WCP) has been commonly used to quantify prediction uncertainty under covariate shift. However, the effectiveness of WCP relies heavily on the degree of overlap between the training and test covariate distributions. This challenge is exacerbated in multi-source settings with varying covariate distributions, where direct application of WCP can be impractical. In this paper, we address the multi-source setup by leveraging WCP under the assumption of a shared conditional distribution. We investigate two extensions of WCP: (i) a merge-based aggregation of source-specific weighted conformal prediction sets, and (ii) a data-pooling strategy that jointly reweights samples across all sources. Theoretical guarantees are provided for the proposed approaches, and experiments are conducted based on a synthetic regression task and a multi-domain image classification benchmark to validate our proposed methods.