Developing efficient solutions for inference problems in intelligent sensor networks is crucial for the next generation of location, tracking, and mapping services. This paper develops a scalable distributed probabilistic inference algorithm that applies to continuous variables, intractable posteriors and large-scale real-time data in sensor networks. In a centralized setting, variational inference is a fundamental technique for performing approximate Bayesian estimation, in which an intractable posterior density is approximated with a parametric density. Our key contribution lies in the derivation of a separable lower bound on the centralized estimation objective, which enables distributed variational inference with one-hop communication in a sensor network. Our distributed evidence lower bound (DELBO) consists of a weighted sum of observation likelihood and divergence to prior densities, and its gap to the measurement evidence is due to consensus and modeling errors. To solve binary classification and regression problems while handling streaming data, we design an online distributed algorithm that maximizes DELBO, and specialize it to Gaussian variational densities with non-linear likelihoods. The resulting distributed Gaussian variational inference (DGVI) efficiently inverts a $1$-rank correction to the covariance matrix. Finally, we derive a diagonalized version for online distributed inference in high-dimensional models, and apply it to multi-robot probabilistic mapping using indoor LiDAR data.

翻译：开发智能传感器网络中推理问题的高效解决方案对于下一代定位、跟踪和建图服务至关重要。本文提出一种可扩展的分布式概率推断算法，适用于传感器网络中的连续变量、难解后验分布以及大规模实时数据。在集中式场景下，变分推断是近似贝叶斯估计的基础技术，它通过参数化密度函数来近似难解的后验密度。我们的核心贡献在于推导出集中式估计目标的可分离下界，从而在传感器网络中通过单跳通信实现分布式变分推断。所提出的分布式证据下界（DELBO）由观测似然与先验密度散度的加权和组成，其与测量证据之间的差距源于共识误差和建模误差。为解决二分类和回归问题并处理流式数据，我们设计了最大化DELBO的在线分布式算法，并将其特化为具有非线性似然的高斯变分密度。由此得到的分布式高斯变分推断（DGVI）能够高效处理协方差矩阵的1阶秩校正。最后，我们推导出面向高维模型在线分布式推断的对角化版本，并将其应用于基于室内LiDAR数据的多机器人概率建图。