Federated Martingale Posterior Samping

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.

arXiv comment5 pages