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I am wondering why some methods transform the underlying graphical model (Bayesian Network for example) to a junction tree¹? What are the advantages? Also what are the limitations?

I believe it's for computational purposes. If that's the case under what circumstances it is not recommended to transform the underlying DAG to joint-trees?

Edit: speaking about graphical models in general (whether they are probabilistic or not), is there some guidelines when to transform them i.e. decompose them?

1 Junction trees are also known as tree decomposition.

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I view junction trees as basically an implementation/analysis tool for doing exact MAP and marginal inference in graphical models. They are needed so that you can safely localize the effects of of maxing or summing (in the case of MAP and marginal inference) out a variable.

When wouldn't you use a junction tee? Well, that's the same case as when you wouldn't do exact inference in your model. Why wouldn't you do exact inference? In general, because it can be expensive; it's exponential in the treewidth of your junction tree.

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    $\begingroup$ But You can do exact inference without junction trees (i.e. through variable elimination and arc reversal). $\endgroup$
    – seteropere
    Nov 27, 2012 at 16:36

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