# Multi-source conformal prediction: leveraging heterogeneity via localization

arXiv: https://arxiv.org/abs/2609.14531 · HTML: https://mlsanity.com/paper/2609.14531/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 59 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Builds on (most cited first, 30 of 39)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [SatMAE: Pre-training Transformers for Temporal and Multi-Spectral Satellite Imagery](https://mlsanity.com/paper/2207.08051/) (2022)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Uncertainty as a Form of Transparency: Measuring, Communicating, and Using Uncertainty](https://mlsanity.com/paper/2011.07586/) (2020)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Class-Conditional Conformal Prediction with Many Classes](https://mlsanity.com/paper/2306.09335/) (2023)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Self-attention for raw optical Satellite Time Series Classification](https://mlsanity.com/paper/1910.10536/) (2019)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Selection and Aggregation of Conformal Prediction Sets](https://mlsanity.com/paper/2104.13871/) (2021)
- [Conformal prediction with local weights: randomization enables local guarantees](https://mlsanity.com/paper/2310.07850/) (2023)
- [Federated Conformal Predictors for Distributed Uncertainty Quantification](https://mlsanity.com/paper/2305.17564/) (2023)
- [Distribution-Free Prediction Sets for Two-Layer Hierarchical Models](https://mlsanity.com/paper/1809.07441/) (2018)
- [Federated Learning for Privacy Preservation in Smart Healthcare Systems: A Comprehensive Survey](https://mlsanity.com/paper/2203.09702/) (2022)
- [One-Shot Federated Conformal Prediction](https://mlsanity.com/paper/2302.06322/) (2023)
- [Distribution-free inference with hierarchical data](https://mlsanity.com/paper/2306.06342/) (2023)
- [Wasserstein-regularized Conformal Prediction under General Distribution Shift](https://mlsanity.com/paper/2501.13430/) (2025)
- [Group-Weighted Conformal Prediction](https://mlsanity.com/paper/2401.17452/) (2024)
- [Conformal prediction after data-dependent model selection](https://mlsanity.com/paper/2408.07066/) (2024)

## Abstract (arXiv)

Many modern prediction tasks involve data from multiple heterogeneous sources, while the test distribution may differ substantially from any individual source. Although heterogeneity poses challenges, it also offers an opportunity: different sources may provide complementary information, with some regions of the feature space better represented in one source than another. We propose Multi-Source Randomly Localized Conformal Prediction (MS-RLCP), which builds on the local coverage properties of randomly localized conformal prediction (RLCP) (Hore and Barber, 2025) and extends it to multiple sources through data-adaptive source selection. Under the widely adopted assumption of a shared response distribution conditional on the features across sources and the test population, we establish finite-sample coverage bounds using an interpretable notion of envelope distribution that captures their aggregate feature-space representation. Our analysis allows the test feature distribution to be absolutely continuous with respect to the envelope, extending beyond mixtures of source distributions. Under additional regularity conditions, we also establish asymptotic test-conditional coverage. Simulations and real-world experiments demonstrate the effectiveness of MS-RLCP across varying levels of data heterogeneity.