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传感器网络中的分布式贝叶斯估计算法。我们面临的挑战包括：(i) 在连续变量概率分布的函数空间中推导出具有可证明正确性的分布式算法，以及(ii) 利用这些结果获得仅基于个体智能体观测变量子集的分布式估计新方法。该方法与协同定位和联邦学习等应用场景相关——在这些场景中，各智能体收集的数据仅依赖于全部兴趣变量的子集。我们提出了利用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、分布式和边缘分布式三种设置。在建立分布式估计目标后，我们证明了各智能体几乎必然收敛到最优概率密度函数集。随后，我们针对仅在各智能体相关变量上估计密度的存储感知算法证明了同样的收敛性。最后，我们提出这些算法的高斯版本，并在建图问题中利用变分推理实现该算法，以处理与LiDAR感知相关的非线性似然模型。