Convergence Analysis of Gaussian SPAWN under High-Order Graphical Models

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.