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This research introduces Federated Martingale Posterior (FMP) sampling, a novel protocol that eliminates the need for difficult prior specification in federated Bayesian neural networks by leveraging predictive distributions instead. The method achieves centralized-level accuracy and superior calibration error while operating as a one-shot, parallelizable process suitable for distributed data environments.
Federated Martingale Posterior Samping
arXiv:2605.18554v2 Announce Type: replace 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.
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.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2605.18554 [cs.LG]
(or arXiv:2605.18554v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.18554 Focus to learn more arXiv-issued DOI via DataCite
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