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Center for Nonlinear Studies |
In this seminar, I will discuss inference in probabilistic graphical models and the heuristic method of belief propagation. We give a graphical interpretation of inference as computing sums or products over walks and orbits (equivalence classes of closed, aperiodic walks) where the weight of a walk is given by a product of edge weights in the graphical model. This point of view has its origins in graph theory (determinant representation of the Ihara zeta function of a graph) and analysis of inference in Gaussian graphical models. We also describe results that point the way towards similar analysis in binary-variable graphical models, based on Feynman's interpretation of the Kac-Ward determinant representation of the partition function of the planar Ising model and generalizations of this representation to higher-genus graphs due to Martin Loebl.
Host: Peter Loxley, loxley@lanl.gov