Recursive FMP for distributed inference in Gaussian graphical models

For inference in Gaussian graphical models with cycles, loopy belief propagation (LBP) performs well for some graphs, but often diverges or has slow convergence. When LBP does converge, the variance estimates are incorrect in general. The feedback message passing (FMP) algorithm has been proposed to enhance the convergence and accuracy of inference. In FMP, standard LBP is run twice on the subgraph excluding the pseudo-FVS (a set of nodes that breaks most crucial cycles) while nodes in the pseudo-FVS use a different protocol. In this paper, we propose recursive FMP, a purely distributed extension of FMP, where all nodes use the same message-passing protocol. An inference problem on the entire graph is recursively reduced to those on smaller subgraphs in a distributed manner. One advantage of this recursive approach compared with FMP is that there is only one active feedback node at a time, so centralized communication among feedback nodes can be turned into message broadcasting from the single feedback node. We characterize this algorithm using walk-sum analysis and provide theoretical results for convergence and accuracy. We also demonstrate the performance using both simulated models on grids and large-scale sea surface height anomaly data.