A Unifying View of Message Passing algorithms for Gaussian MRFs

We illustrate the relationship between message passing algorithms in GMRFs and matrix factorization algorithms. Specifically, we show that message passing on trees is equivalent to Gaussian elimination, while Loopy Belief Propagation is equivalent to Gauss-Seidel relaxation. Similarly, recently introduced message passing algorithms such as the Extended Message Passing, and the Embedded Subgraphs algorithm are also shown to be equivalent to commonly known matrix methods. We describe efficient extensions to message passing algorithms based on exploiting these relationships.