Graph-Enabled Efficient Federated Bayesian Modeling

Federated Bayesian modeling requires combining evidence from distributed users into a coherent global posterior while keeping users' raw data on-device. We propose Federated Latent Graph MCMC (FLaG-MCMC), a computationally efficient framework for federated learning in which historical posterior samples of a shared global parameter are encoded into a learned low-dimensional latent space, connected via a $k$-nearest-neighbor graph, and transferred sequentially to new users as a nonparametric prior. Each user runs graph-based MCMC in the latent space guided by their own likelihood, returns updated global samples to the server, and retains local latent variables on-device. We demonstrate FLaG-MCMC on Bayesian meta-analysis for opioid use disorder prevalence estimation and on federated topic modeling, where the federated posterior closely approximates the pooled full-data posterior for both global parameters and local user-level inference.