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：我们考虑在以要素图为代表并通过高斯信仰传播算法解决的线性模型中进行最大可能性估计的问题。在大型事物互联网(IoT)网络和边缘计算驱动下,我们将上述问题设置在分组假设中,将系数图分为组,并分配在一些边缘计算节点中以分布方式处理。关于这些假设,我们表明一种交替的高斯信仰传播算法(AGBP),这种算法在组际和组内迭代之间互换,表明与文献中的现有解决办法相比,趋同特性的优异性。我们提出了一个全面框架,并引入了适当的指标,以分析以对称和非对称、正方和矩形矩阵为特征的广泛线性模型。我们将分析扩大到动态线性模型的情况,采用动态新数据随着时间的推移的到达。我们结合了分析和广泛的数字结果,展示了AGBP算法的效率和可扩展性,使它成为大规模IOT网络大规模推价的适当解决办法。