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On the Optimality of Solutions of the MaxProduct Belief Propagation Algorithm in Arbitrary Graphs
, 2001
"... Graphical models, suchasBayesian networks and Markov random fields, represent statistical dependencies of variables by a graph. The maxproduct "belief propagation" algorithm is a localmessage passing algorithm on this graph that is known to converge to a unique fixed point when the graph is a tr ..."
Abstract

Cited by 185 (15 self)
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Graphical models, suchasBayesian networks and Markov random fields, represent statistical dependencies of variables by a graph. The maxproduct "belief propagation" algorithm is a localmessage passing algorithm on this graph that is known to converge to a unique fixed point when the graph is a tree. Furthermore, when the graph is a tree, the assignment based on the fixedpoint yields the most probable a posteriori (MAP) values of the unobserved variables given the observed ones. Recently, good
Geometric Modelling with αComplexes
, 2000
"... The shape of real objects can be so complicated, that only a sampling data point set can accurately represent them. Analytic descriptions are too complicated or impossible. ..."
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The shape of real objects can be so complicated, that only a sampling data point set can accurately represent them. Analytic descriptions are too complicated or impossible.