Gaussian belief propagation (BP) is widely used for distributed inference. Its computational complexity, and communication overhead depend on the total number of messages updated, and transmitted among variable nodes, respectively. For large, and dense networks, both computational complexity, and communication overhead could be extremely high. To this end, a variant of Gaussian BP called Gaussian SPAWN (sum-product algorithm over a wireless network) could be applied, where outgoing messages are approximated by beliefs. Similar to Gaussian BP, the convergence of Gaussian SPAWN is not guaranteed for loopy graphs. Therefore, we analyze the convergence of belief means, and variances in Gaussian SPAWN. Numerical results are presented to corroborate the newly established theories and a comparison of Gaussian BP, and Gaussian SPAWN is illustrated.

中文翻译：

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高阶图模型下Gaussian SPAWN的收敛性分析

高斯置信传播 (BP) 广泛用于分布式推理。它的计算复杂度和通信开销分别取决于在变量节点之间更新和传输的消息总数。对于大型且密集的网络，计算复杂度和通信开销都可能非常高。为此，可以应用一种称为 Gaussian SPAWN（无线网络上的和积算法）的高斯 BP 变体，其中传出消息由信念近似。与高斯 BP 类似，高斯 SPAWN 的收敛性不能保证用于循环图。因此，我们分析了信念均值的收敛性，以及高斯 SPAWN 中的方差。数值结果证实了新建立的理论和高斯 BP 的比较，并说明了高斯 SPAWN。