We consider the problem of maximum likelihood estimation in linear models represented by factor graphs and solved via the Gaussian belief propagation algorithm. Motivated by massive internet of things (IoT) networks and edge computing, we set the above problem in a clustered scenario, where the factor graph is divided into clusters and assigned for processing in a distributed fashion across a number of edge computing nodes. For these scenarios, we show that an alternating Gaussian belief propagation (AGBP) algorithm that alternates between inter- and intra-cluster iterations, demonstrates superior performance in terms of convergence properties compared to the existing solutions in the literature. We present a comprehensive framework and introduce appropriate metrics to analyse AGBP algorithm across a wide range of linear models characterised by symmetric and non-symmetric, square, and rectangular matrices. We extend the analysis to the case of dynamic linear models by introducing dynamic arrival of new data over time. Using a combination of analytical and extensive numerical results, we show the efficiency and scalability of AGBP algorithm, making it a suitable solution for large-scale inference in massive IoT networks.

翻译：我们考虑以因子图表示、通过高斯置信传播算法求解的线性模型中的最大似然估计问题。受大规模物联网网络和边缘计算的驱动，我们在聚类场景中设定上述问题：将因子图划分为若干聚类，并分配给多个边缘计算节点进行分布式处理。针对此类场景，我们证明：交替高斯置信传播算法通过在聚类间与聚类内迭代之间交替进行，在收敛性能方面优于现有文献中的解决方案。我们提出了一个综合框架，并引入适当的度量指标，以分析该算法在对称/非对称、方阵/矩形矩阵等各类线性模型中的表现。通过引入随时间动态到达的新数据，我们将分析扩展至动态线性模型情形。结合理论分析与大量数值实验结果，我们展示了交替高斯置信传播算法的高效性与可扩展性，使其成为大规模物联网网络中大规模推断问题的理想解决方案。