ABSTRACT
One of the strengths of graphical models is that they provide methods for calculating a margin of the graphical belief function without the need for calculating the joint distribution of all the variables. This is the role of the fusion and propagation algorithm. The fusion and propagation algorithm merges ideas from the fusion and propagation algorithm of Pearl and the peeling algorithm. The fusion and propagation algorithm calculates marginal distributions by propagating messages throughout the tree. Fusion and propagation works by the following device: the sum of the local information and the messages received is the same as the sum of all of the components of the tree model, which is in turn the sum of all of the components of the graphical model. Fortunately, the fusion and propagation algorithm can use any Markov tree, not just the tree of cliques.
