# Federated Martingale Posterior Samping

arXiv: https://arxiv.org/abs/2605.18554 · HTML: https://mlsanity.com/paper/2605.18554/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 24 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 19 of 19)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition](https://mlsanity.com/paper/1310.1531/) (2013)
- [Meta-Dataset: A Dataset of Datasets for Learning to Learn from Few Examples](https://mlsanity.com/paper/1903.03096/) (2019)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Functional Variational Bayesian Neural Networks](https://mlsanity.com/paper/1903.05779/) (2019)
- [Martingale posterior distributions](https://mlsanity.com/paper/2103.15671/) (2021)
- [Federated Generalized Bayesian Learning via Distributed Stein Variational Gradient Descent](https://mlsanity.com/paper/2009.06419/) (2020)
- [FedLPA: One-shot Federated Learning with Layer-Wise Posterior Aggregation](https://mlsanity.com/paper/2310.00339/) (2023)
- [Martingale Posterior Neural Processes](https://mlsanity.com/paper/2304.09431/) (2023)
- [Federated Inference with Reliable Uncertainty Quantification over Wireless Channels via Conformal Prediction](https://mlsanity.com/paper/2308.04237/) (2023)
- [Robust PACm: Training Ensemble Models Under Misspecification and Outliers](https://mlsanity.com/paper/2203.01859/) (2022)
- [Bayesian Predictive Inference Beyond Martingales](https://mlsanity.com/paper/2507.21874/) (2025)
- [Bayesian Deep Learning Via Expectation Maximization and Turbo Deep Approximate Message Passing](https://mlsanity.com/paper/2402.07366/) (2024)
- [Uncertainty Quantification and Data Efficiency in AI: An Information-Theoretic Perspective](https://mlsanity.com/paper/2512.05267/) (2025)
- [One-Shot Federated Learning with Bayesian Pseudocoresets](https://mlsanity.com/paper/2406.02177/) (2024)

## Abstract (arXiv)

Federated Bayesian neural networks require fixing a prior on the model parameters, which is notoriously difficult, and misspecification of this prior can severely degrade accuracy and calibration. Motivated by the rapid progress of predictive models, the martingale posterior, also known as predictive Bayes, replaces the prior--likelihood pair with a predictive distribution and recovers parameter uncertainty by repeatedly drawing predictive samples and refitting the model. This letter proposes {federated martingale posterior} (FMP) sampling, a one-shot embarrassingly parallel protocol in which each client uploads a small set of trainable data embeddings and the server runs the predictive sampler centrally. Analysis of the sampling error demonstrates the impact of the dataset compression rate, while experiments show that FMP closely matches the centralized counterpart and achieves the lowest mean expected calibration error (ECE) among the evaluated one-shot federated methods.