scholarly journals Fast Generalized Belief Propagation for MAP Estimation on 2D and 3D Grid-Like Markov Random Fields

2008 ◽  
pp. 41-50 ◽  
Author(s):  
Kersten Petersen ◽  
Janis Fehr ◽  
Hans Burkhardt
Keyword(s):  
Random Fields ◽  
Markov Random Fields ◽  
Belief Propagation ◽  
Map Estimation ◽  
Markov Random ◽  
2D And 3D

Efficient Belief Propagation with Learned Higher-Order Markov Random Fields

2006 ◽  
pp. 269-282 ◽  
Author(s):  
Xiangyang Lan ◽  
Stefan Roth ◽  
Daniel Huttenlocher ◽  
Michael J. Black
Keyword(s):  
Random Fields ◽  
Markov Random Fields ◽  
Belief Propagation ◽  
Higher Order ◽  
Markov Random

scholarly journals Convexity Arguments for Efficient Minimization of the Bethe and Kikuchi Free Energies

2006 ◽  
Vol 26 ◽  
pp. 153-190 ◽  
Author(s):  
T. Heskes
Keyword(s):  
Free Energy ◽  
Random Fields ◽  
Markov Random Fields ◽  
Belief Propagation ◽  
Helmholtz Free Energy ◽  
Upper Bounds ◽  
Free Energies ◽  
Markov Random ◽  
Bethe Free Energy ◽  
Constrained Minimization Problem

Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms have been shown to correspond to extrema of the Bethe and Kikuchi free energy, both of which are approximations of the exact Helmholtz free energy. However, belief propagation does not always converge, which motivates approaches that explicitly minimize the Kikuchi/Bethe free energy, such as CCCP and UPS. Here we describe a class of algorithms that solves this typically non-convex constrained minimization problem through a sequence of convex constrained minimizations of upper bounds on the Kikuchi free energy. Intuitively one would expect tighter bounds to lead to faster algorithms, which is indeed convincingly demonstrated in our simulations. Several ideas are applied to obtain tight convex bounds that yield dramatic speed-ups over CCCP.

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