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I am wondering why some methods transform the underlying DAG-based graphical model (Bayesian Networks for example) to a joint tree$^1$? What are the advantages?

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 jointtrees?

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


$^1$ Also known as jointree, junction tree, tree decomposition.

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