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.

翻译：联邦贝叶斯建模需要将来自分布式用户的证据整合为一致的全局后验分布，同时保留用户原始数据在终端设备上。我们提出联邦潜在图马尔可夫链蒙特卡洛方法（FLaG-MCMC），这是一种计算高效的联邦学习框架：将共享全局参数的历史后验样本编码到经学习的低维潜在空间中，通过$k$-近邻图进行连接，并作为非参数先验依次传递至新用户。每个用户在潜在空间中基于自身似然执行图驱动MCMC，将更新后的全局样本返回服务器，并在终端设备上保留局部潜在变量。我们在面向阿片类药物使用障碍患病率估算的贝叶斯元分析以及联邦主题建模中验证了FLaG-MCMC——联邦后验分布能够高度逼近汇集完整数据的后验分布，实现全局参数与局部用户级推断的一致拟合。