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I know Bayesian or Directed Graphical models are good for fast inference using message passing techniques. But how does it work with undirected models? With directed models, you moralize the graph making it an undirected and triangular graph whose cliques are connected in a junction tree thus allowing the message passing.

If you start out with a triangulated undirected model, you just go right to the junction tree and skip the moralization. But what if it is not triangulated? If you triangulate this, it becomes a different model. Can you do fast inference with undirected models that are not triangulated?

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What you're looking for are Markov Random Fields which are, basically, what you've constructed as the triangular graph. One reason why they are studied separately is due to the fact that it makes sense (in some contexts) to discuss undirected graphical models that are not triangulated. The key feature is that, whether or not the graph has been triangulated, you identify the cliques in the undirected graph, and then associate potential functions with them.

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  • $\begingroup$ So does there exist fast, message-passing algorithms for inference in these kind of un-triangulated graphs or do you have to resort to something like Gibbs sampling? $\endgroup$ – Dave31415 Mar 1 '14 at 20:06
  • $\begingroup$ Yes, the message passing in the clique tree is exactly the same. $\endgroup$ – Dave Mar 2 '14 at 1:06

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