Recursive Algorithms for Approximating Probabilities in Graphical Models

Part of Advances in Neural Information Processing Systems 9 (NIPS 1996)

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Tommi Jaakkola, Michael Jordan


We develop a recursive node-elimination formalism for efficiently approximating large probabilistic networks. No constraints are set on the network topologies. Yet the formalism can be straightfor(cid:173) wardly integrated with exact methods whenever they are/become applicable. The approximations we use are controlled: they main(cid:173) tain consistently upper and lower bounds on the desired quantities at all times. We show that Boltzmann machines, sigmoid belief networks, or any combination (i.e., chain graphs) can be handled within the same framework. The accuracy of the methods is veri(cid:173) fied experimentally.