Exploiting Within-Clique Factorizations in Junction-Tree Algorithms

We show that the expected computational complexity of the Junction-Tree Algorithm for maximum a posteriori inference in graph-ical models can be improved. Our results apply whenever the potentials over maximal cliques of the triangulated graph are factored over subcliques. This is common in many real applications, as we illustrate with several ex-amples. The new algorithms are easily im-plemented, and experiments show substantial speed-ups over the classical Junction-Tree Al-gorithm. This enlarges the class of models for which exact inference is efficient.