# Multi-Source Conformal Inference Under Distribution Shift

arXiv: https://arxiv.org/abs/2405.09331 · HTML: https://mlsanity.com/paper/2405.09331/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 15 May 2024.

## Builds on (most cited first, 24 of 24)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [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)
- [Semiparametric counterfactual density estimation](https://mlsanity.com/paper/2102.12034/) (2021)
- [Conformal Sensitivity Analysis for Individual Treatment Effects](https://mlsanity.com/paper/2112.03493/) (2021)
- [Doubly Robust Calibration of Prediction Sets under Covariate Shift](https://mlsanity.com/paper/2203.01761/) (2022)
- [Diagnosing Model Performance Under Distribution Shift](https://mlsanity.com/paper/2303.02011/) (2023)
- [Distribution-Free Prediction Sets for Two-Layer Hierarchical Models](https://mlsanity.com/paper/1809.07441/) (2018)
- [Conformal Prediction for Federated Uncertainty Quantification Under Label Shift](https://mlsanity.com/paper/2306.05131/) (2023)
- [One-Shot Federated Conformal Prediction](https://mlsanity.com/paper/2302.06322/) (2023)
- [Federated Causal Inference in Heterogeneous Observational Data](https://mlsanity.com/paper/2107.11732/) (2021)
- [Targeting Underrepresented Populations in Precision Medicine: A Federated Transfer Learning Approach](https://mlsanity.com/paper/2108.12112/) (2021)
- [An Adaptive Kernel Approach to Federated Learning of Heterogeneous Causal Effects](https://mlsanity.com/paper/2301.00346/) (2023)
- [Federated Adaptive Causal Estimation (FACE) of Target Treatment Effects](https://mlsanity.com/paper/2112.09313/) (2021)
- [Distribution-free inference with hierarchical data](https://mlsanity.com/paper/2306.06342/) (2023)
- [Multiply Robust Federated Estimation of Targeted Average Treatment Effects](https://mlsanity.com/paper/2309.12600/) (2023)
- [Robust Inference for Federated Meta-Learning](https://mlsanity.com/paper/2301.00718/) (2023)
- [Diagnosing the role of observable distribution shift in scientific replications](https://mlsanity.com/paper/2309.01056/) (2023)
- [Privacy-Preserving, Communication-Efficient, and Target-Flexible Hospital Quality Measurement](https://mlsanity.com/paper/2203.00768/) (2022)

## Built on by (most cited first, 11 of 11)

- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Wasserstein-regularized Conformal Prediction under General Distribution Shift](https://mlsanity.com/paper/2501.13430/) (2025)
- [What If We Had Used a Different App? Reliable Counterfactual KPI Analysis in Wireless Systems](https://mlsanity.com/paper/2410.00150/) (2024)
- [Conformal Prediction Under Generalized Covariate Shift with Posterior Drift](https://mlsanity.com/paper/2502.17744/) (2025)
- [Conformal Prediction in The Loop: A Feedback-Based Uncertainty Model for Trajectory Optimization](https://mlsanity.com/paper/2510.16376/) (2025)
- [Federated Conditional Conformal Prediction via Generative Models](https://mlsanity.com/paper/2510.13297/) (2025)
- [Multi-Distribution Robust Conformal Prediction](https://mlsanity.com/paper/2601.02998/) (2026)
- [Rate doubly robust estimation for weighted average treatment effects](https://mlsanity.com/paper/2509.14502/) (2025)
- [IDOL: Meeting Diverse Distribution Shifts with Prior Physics for Tropical Cyclone Multi-Task Estimation](https://mlsanity.com/paper/2511.11750/) (2025)
- [Debiased Machine Learning for Conformal Prediction of Counterfactual Outcomes Under Runtime Confounding](https://mlsanity.com/paper/2604.03772/) (2026)
- [Multi-source conformal prediction: leveraging heterogeneity via localization](https://mlsanity.com/paper/2609.14531/) (2026)

## Abstract (arXiv)

Recent years have experienced increasing utilization of complex machine learning models across multiple sources of data to inform more generalizable decision-making. However, distribution shifts across data sources and privacy concerns related to sharing individual-level data, coupled with a lack of uncertainty quantification from machine learning predictions, make it challenging to achieve valid inferences in multi-source environments. In this paper, we consider the problem of obtaining distribution-free prediction intervals for a target population, leveraging multiple potentially biased data sources. We derive the efficient influence functions for the quantiles of unobserved outcomes in the target and source populations, and show that one can incorporate machine learning prediction algorithms in the estimation of nuisance functions while still achieving parametric rates of convergence to nominal coverage probabilities. Moreover, when conditional outcome invariance is violated, we propose a data-adaptive strategy to upweight informative data sources for efficiency gain and downweight non-informative data sources for bias reduction. We highlight the robustness and efficiency of our proposals for a variety of conformal scores and data-generating mechanisms via extensive synthetic experiments. Hospital length of stay prediction intervals for pediatric patients undergoing a high-risk cardiac surgical procedure between 2016-2022 in the U.S. illustrate the utility of our methodology.