Generalized Belief Propagation

In an important recent paper, Yedidia, Freeman, and Weiss [11] showed that there is a close connection between the belief propagation algorithm for probabilistic inference and the Bethe-Kikuchi approximation to the variational free energy in statistical physics. Using this connection, they generalized the belief propagation algorithms to a "region based" belief propagation algorithm. Subsequently, Aji and McEliece [2] used these methods to prove a similar statement for the "Generalized Distributive Law" [1] applied to a junction graph. In this thesis, we will show further generalizations of the belief propagation algorithms using a poset. Our main result is that if the GGBP is applied to Hasse diagram, the fixed points of the algorithm are in one-to-one correspondence with the stationary points of a certain Bethe-Kikuchi free energy. I would like to thank Prof. Robert J. McEliece for his continuous support and help. He had a great confidence in me, and he directed ...

• Type: Conference
• Year: 2000
• Where: NIPS
• Authors: Jonathan S. Yedidia, William T. Freeman, Yair Weiss
• Keywords: Belief Propagation Algorithms, Free Energy, NIPS 2000, NIPS 2007, Variational Free Energy