图启用的高效联邦贝叶斯建模
Graph-Enabled Efficient Federated Bayesian Modeling
AI总结：
提出FLaG-MCMC框架，通过将历史后验样本编码到低维潜在空间并构建k近邻图，实现高效联邦贝叶斯学习，在阿片类药物使用障碍患病率估计和联邦主题建模中验证了其近似全局后验的能力。
摘要：
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，同时将用户的原始数据保留在设备上。我们提出了联邦潜在图MCMC（FLaG-MCMC），这是一个计算高效的联邦学习框架，其中共享全局参数的历史后验样本被编码到学习到的低维潜在空间中，通过$k$-近邻图连接，并作为非参数先验顺序传递给新用户。每个用户在其自身似然的引导下，在潜在空间中运行基于图的MCMC，将更新的全局样本返回给服务器，并将局部潜在变量保留在设备上。我们在阿片类药物使用障碍患病率估计的贝叶斯元分析和联邦主题建模上展示了FLaG-MCMC，其中联邦后验在全局参数和局部用户级推断上均紧密逼近合并的全数据后验。
英文摘要：
Federated Bayesian modeling requires combining evidence across distributed data holders while preserving posterior uncertainty and keeping local data decentralized. We propose Federated Latent Graph MCMC (FLaG-MCMC), a framework for sequential posterior transfer in which accumulated posterior information is represented by a reservoir of Monte Carlo samples. FLaG-MCMC constructs a graph that captures the geometry of the posterior reservoir and uses graph-enabled proposals whose per-iteration cost is independent of the reservoir size. Each data holder updates the inherited posterior using its local likelihood and returns an updated reservoir for subsequent inference. We apply FLaG-MCMC in two health science settings. Using mobile and wearable device data from GLOBEM, we investigate associations between depression status and behavioral patterns while sequentially accumulating posterior information across participants. FLaG-MCMC accurately reconstructs the corresponding pooled Bayesian posterior while closely tracking evolving posterior location and uncertainty in these associations. We also conduct a simulation study motivated by Bayesian evidence synthesis for opioid use disorder prevalence across studies, transferring posterior information from an Ohio study to a subsequent New York analysis under covariate shift. In this setting, FLaG-MCMC demonstrates reliable posterior transfer and favorable computational scaling. Theoretical results establish the validity and consistency of the framework.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
