# Distributed Conformal Prediction via Message Passing

arXiv: https://arxiv.org/abs/2501.14544 · HTML: https://mlsanity.com/paper/2501.14544/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 38 references that are in the map.
- First posted on arXiv 24 Jan 2025.

## Builds on (most cited first, 28 of 28)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Language Models with Conformal Factuality Guarantees](https://mlsanity.com/paper/2402.10978/) (2024)
- [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)
- [On the Linear Convergence of the ADMM in Decentralized Consensus Optimization](https://mlsanity.com/paper/1307.5561/) (2013)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Federated Conformal Predictors for Distributed Uncertainty Quantification](https://mlsanity.com/paper/2305.17564/) (2023)
- [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)
- [Localized Adaptive Risk Control](https://mlsanity.com/paper/2405.07976/) (2024)
- [On the O(1/k) Convergence of Asynchronous Distributed Alternating Direction Method of Multipliers](https://mlsanity.com/paper/1307.8254/) (2013)
- [Achieving Linear Convergence in Distributed Asynchronous Multi-agent Optimization](https://mlsanity.com/paper/1803.10359/) (2018)
- [Bayesian Optimization with Formal Safety Guarantees via Online Conformal Prediction](https://mlsanity.com/paper/2306.17815/) (2023)
- [Federated Inference with Reliable Uncertainty Quantification over Wireless Channels via Conformal Prediction](https://mlsanity.com/paper/2308.04237/) (2023)
- [Generalization and Informativeness of Conformal Prediction](https://mlsanity.com/paper/2401.11810/) (2024)
- [Certifiably Byzantine-Robust Federated Conformal Prediction](https://mlsanity.com/paper/2406.01960/) (2024)
- [Conformal Distributed Remote Inference in Sensor Networks Under Reliability and Communication Constraints](https://mlsanity.com/paper/2409.07902/) (2024)
- [Building Conformal Prediction Intervals with Approximate Message Passing](https://mlsanity.com/paper/2410.16493/) (2024)

## Built on by (most cited first, 4 of 4)

- [AutoSOTA: An End-to-End Automated Research System for State-of-the-Art AI Model Discovery](https://mlsanity.com/paper/2604.05550/) (2026)
- [Efficient Federated Conformal Prediction with Group-Conditional Guarantee](https://mlsanity.com/paper/2603.14198/) (2026)
- [Federated Conditional Conformal Prediction via Generative Models](https://mlsanity.com/paper/2510.13297/) (2025)
- [Robust Conditional Conformal Prediction via Branched Normalizing Flow](https://mlsanity.com/paper/2605.01868/) (2026)

## Abstract (arXiv)

Post-hoc calibration of pre-trained models is critical for ensuring reliable inference, especially in safety-critical domains such as healthcare. Conformal Prediction (CP) offers a robust post-hoc calibration framework, providing distribution-free statistical coverage guarantees for prediction sets by leveraging held-out datasets. In this work, we address a decentralized setting where each device has limited calibration data and can communicate only with its neighbors over an arbitrary graph topology. We propose two message-passing-based approaches for achieving reliable inference via CP: quantile-based distributed conformal prediction (Q-DCP) and histogram-based distributed conformal prediction (H-DCP). Q-DCP employs distributed quantile regression enhanced with tailored smoothing and regularization terms to accelerate convergence, while H-DCP uses a consensus-based histogram estimation approach. Through extensive experiments, we investigate the trade-offs between hyperparameter tuning requirements, communication overhead, coverage guarantees, and prediction set sizes across different network topologies. The code of our work is released on: https://github.com/HaifengWen/Distributed-Conformal-Prediction.