Understanding Belief Propagation and its Generalizations Part 1

This paper did a wonderful job of showing how belief propagation has been applied to a variety of graphical models in a variety of disciplines. It is very clearly written.

The first part of the paper discussed the conversions between and resulting equality of factor graphs, directed graphs and undirected graphs (as well as a few other techniques). Here is a brief summary of the conversion from a directed graph to an undirected graph.

Then the paper proceeded to describe belief propagation on the undirected graphical model. Although the paper didn't mention it, the discussion group that read this paper explained what loopy belief propagation as a consequence. A short summary of that discussion is here.