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PreprintarXiv licencearXiv

Federated Martingale Posterior Samping

  • Boning Zhang
  • Matteo Zecchin
  • Mingzhao Guo
  • Dongzhu Liu
  • Osvaldo Simeone
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026federated,
  title = {{Federated Martingale Posterior Samping}},
  author = {Boning Zhang and Matteo Zecchin and Mingzhao Guo and Dongzhu Liu and Osvaldo Simeone},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.18554},
  eprint = {2605.18554},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.18554},
}
RIS
TY  - UNPB
TI  - Federated Martingale Posterior Samping
AU  - Boning Zhang
AU  - Matteo Zecchin
AU  - Mingzhao Guo
AU  - Dongzhu Liu
AU  - Osvaldo Simeone
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2605.18554
UR  - https://arxiv.org/abs/2605.18554
AB  - 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.
ER  -