# Multi-Distribution Robust Conformal Prediction

arXiv: https://arxiv.org/abs/2601.02998 · HTML: https://mlsanity.com/paper/2601.02998/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 59 references that are in the map.
- First posted on arXiv 6 Jan 2026.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Agnostic Federated Learning](https://mlsanity.com/paper/1902.00146/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Fairness without Demographics through Adversarially Reweighted Learning](https://mlsanity.com/paper/2006.13114/) (2020)
- [BREEDS: Benchmarks for Subpopulation Shift](https://mlsanity.com/paper/2008.04859/) (2020)
- [Minimax Pareto Fairness: A Multi Objective Perspective](https://mlsanity.com/paper/2011.01821/) (2020)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Change is Hard: A Closer Look at Subpopulation Shift](https://mlsanity.com/paper/2302.12254/) (2023)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach](https://mlsanity.com/paper/2111.12161/) (2021)
- [Federated Conformal Predictors for Distributed Uncertainty Quantification](https://mlsanity.com/paper/2305.17564/) (2023)
- [With Malice Towards None: Assessing Uncertainty via Equalized Coverage](https://mlsanity.com/paper/1908.05428/) (2019)
- [Conformal Sensitivity Analysis for Individual Treatment Effects](https://mlsanity.com/paper/2112.03493/) (2021)
- [Bounds on the conditional and average treatment effect with unobserved confounding factors](https://mlsanity.com/paper/1808.09521/) (2018)
- [Proxy Fairness](https://mlsanity.com/paper/1806.11212/) (2018)
- [One-Shot Federated Conformal Prediction](https://mlsanity.com/paper/2302.06322/) (2023)

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

- [Certify or Refuse: A Cross-Model Map for Selective Risk Control with Coverage Floors under Covariate Shift](https://mlsanity.com/paper/2608.10893/) (2026)
- [Multi-source conformal prediction: leveraging heterogeneity via localization](https://mlsanity.com/paper/2609.14531/) (2026)

## Abstract (arXiv)

In many fairness and distribution robustness problems, one has access to labeled data from multiple source distributions yet the test data may come from an arbitrary member or a mixture of them. We study the problem of constructing a conformal prediction set that is uniformly valid across multiple, heterogeneous distributions, in the sense that no matter which distribution the test point is from, the coverage of the prediction set is guaranteed to exceed a pre-specified level. We first propose a max-p aggregation scheme that delivers finite-sample, multi-distribution coverage given any conformity scores associated with each distribution. Upon studying several efficiency optimization programs subject to uniform coverage, we prove the optimality and tightness of our aggregation scheme, and propose a general algorithm to learn conformity scores that lead to efficient prediction sets after the aggregation under standard conditions. We discuss how our framework relates to group-wise distributionally robust optimization, sub-population shift, fairness, and multi-source learning. In synthetic and real-data experiments, our method delivers valid worst-case coverage across multiple distributions while greatly reducing the set size compared with naively applying max-p aggregation to single-source conformity scores, and can be comparable in size to single-source prediction sets with popular, standard conformity scores.