![]() ![]() The initialization and scheduling of message updates must be adjusted slightly (compared with the previously described schedule for acyclic graphs) because graphs might not contain any leaves. The algorithm is then sometimes called loopy belief propagation, because graphs typically contain cycles, or loops. The algorithm is completed when all leaves have received their messages.Īpproximate algorithm for general graphs Īlthough it was originally designed for acyclic graphical models, the Belief Propagation algorithm can be used in general graphs. The second step involves passing the messages back out: starting at the root, messages are passed in the reverse direction. ![]() This continues until the root has obtained messages from all of its adjoining nodes. The tree structure guarantees that it is possible to obtain messages from all other adjoining nodes before passing the message on. In the first step, messages are passed inwards: starting at the leaves, each node passes a message along the (unique) edge towards the root node. This optimal scheduling can be described as follows:īefore starting, the graph is oriented by designating one node as the root any non-root node which is connected to only one other node is called a leaf. Furthermore, with proper scheduling of the message updates, it will terminate after two full passes through the tree. In the case when the factor graph is a tree, the belief propagation algorithm will compute the exact marginals. This can be shown by mathematical induction. is a tree or a forest), these estimated marginal actually converge to the true marginals in a finite number of iterations. In the case where the factor graph is acyclic (i.e. Given a finite set of discrete random variables X 1, …, X n
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