In this paper, we aim to design and analyze distributed Bayesian estimation algorithms for sensor networks. The challenges we address are to (i) derive a distributed provably-correct algorithm in the functional space of probability distributions over continuous variables, and (ii) leverage these results to obtain new distributed estimators restricted to subsets of variables observed by individual agents. This relates to applications such as cooperative localization and federated learning, where the data collected at any agent depends on a subset of all variables of interest. We present Bayesian density estimation algorithms using data from non-linear likelihoods at agents in centralized, distributed, and marginal distributed settings. After setting up a distributed estimation objective, we prove almost-sure convergence to the optimal set of pdfs at each agent. Then, we prove the same for a storage-aware algorithm estimating densities only over relevant variables at each agent. Finally, we present a Gaussian version of these algorithms and implement it in a mapping problem using variational inference to handle non-linear likelihood models associated with LiDAR sensing.

翻译：本文旨在设计并分析面向传感器网络的分布式贝叶斯估计算法。我们需应对的挑战包括：(i) 在连续变量概率分布的函数空间内推导出具有可证明正确性的分布式算法；(ii) 利用这些成果，针对各智能体所观测的变量子集，推导出新型分布式估计器。这涉及协作定位与联邦学习等应用场景——在这些场景中，任何智能体收集的数据仅依赖于所有关注变量的一个子集。我们提出了基于各智能体非线性似然数据的贝叶斯密度估计算法，涵盖集中式、分布式及边际分布式三种模式。在建立分布式估计目标后，我们证明了各智能体概率密度函数集合几乎必然收敛至最优解，继而证明针对各智能体仅估计相关变量密度的存储感知算法同样具备该收敛性。最后，我们给出这些算法的高斯形式，并通过变分推断处理与激光雷达传感相关的非线性似然模型，将其应用于地图构建问题。