Recursive Algorithms for Approximating Probabilities in Graphical Models

Department of Brain and Cognitive Sciences Massachusetts Institute of Technology Cambridge, MA 02139 Abstract 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 straightforwardly integratedwith exact methods whenever they are/become applicable. The approximations we use are controlled: they maintain consistentlyupper 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.