论文标题
通过分段确定性马尔可夫流程联合贝叶斯计算
Federated Bayesian Computation via Piecewise Deterministic Markov Processes
论文作者
论文摘要
在实践中执行贝叶斯计算时，通常会面临构成模型组件和/或数据仅以分布式方式可用的挑战，例如由于隐私问题或庞大的量。尽管已经提出了在此类联邦设置中执行后验推断的各种方法，但这些方法要么在数据和/或模型上做出非常有力的假设，要么当将局部后期后期组合在一起以形成目标后部的近似值时会引入明显的偏见。通过利用最近开发的基于分段确定性马尔可夫过程（PDMP）的马尔可夫链蒙特卡洛（MCMC）的方法，我们开发了一个计算和沟通 - 有效的后验推理算法（FED-PDMC）的家族，该家族提供了beyes clastic and允许的允许群体和允许的允许的允许的允许的允许的，该算法提供了不可分割的确切的近似值。我们表明，客户与服务器之间的通信通过建立差异隐私保证来保留单个数据源的隐私。我们量化了FED-PDMC在一类说明性分析案例研究中的性能，并在许多合成示例以及逼真的贝叶斯计算基准中证明了其功效。
When performing Bayesian computations in practice, one is often faced with the challenge that the constituent model components and/or the data are only available in a distributed fashion, e.g. due to privacy concerns or sheer volume. While various methods have been proposed for performing posterior inference in such federated settings, these either make very strong assumptions on the data and/or model or otherwise introduce significant bias when the local posteriors are combined to form an approximation of the target posterior. By leveraging recently developed methods for Markov Chain Monte Carlo (MCMC) based on Piecewise Deterministic Markov Processes (PDMPs), we develop a computation -- and communication -- efficient family of posterior inference algorithms (Fed-PDMC) which provides asymptotically exact approximations of the full posterior over a large class of Bayesian models, allowing heterogenous model and data contributions from each client. We show that communication between clients and the server preserves the privacy of the individual data sources by establishing differential privacy guarantees. We quantify the performance of Fed-PDMC over a class of illustrative analytical case-studies and demonstrate its efficacy on a number of synthetic examples along with realistic Bayesian computation benchmarks.
