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1 BELIEF PROPAGATION, MEANFIELD, AND BETHE APPROXIMATIONS
"... This chapter describes methods for estimating the marginals and maximum a posteriori (MAP) estimates of probability distributions defined over graphs by approximate methods including Mean Field Theory (MFT), variational methods, and belief propagation. These methods typically formulate this problem ..."
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This chapter describes methods for estimating the marginals and maximum a posteriori (MAP) estimates of probability distributions defined over graphs by approximate methods including Mean Field Theory (MFT), variational methods, and belief propagation. These methods typically formulate this problem
Understanding the Bethe Approximation: When and How can it go Wrong?
"... Belief propagation is a remarkably effective tool for inference, even when applied to networks with cycles. It may be viewed as a way to seek the minimum of the Bethe free energy, though with no convergence guarantee in general. A variational perspective shows that, compared to exact inference, this ..."
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Cited by 4 (4 self)
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, this minimization employs two forms of approximation: (i) the true entropy is approximated by the Bethe entropy, and (ii) the minimization is performed over a relaxation of the marginal polytope termed the local polytope. Here we explore when and how the Bethe approximation can fail for binary pairwise models
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 585 (13 self)
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that is exact when the factor graph is a tree, but only approximate when the factor graph has cycles. We show that BP fixed points correspond to the stationary points of the Bethe approximation of the free energy for a factor graph. We explain how to obtain regionbased free energy approximations that improve
Inference in Boltzmann Machines, Mean Field, TAP and Bethe Approximations
"... Inference in Boltzmann machines is NPhard in general. As a result approximations are often necessary. We review the mean field and TAP approximations as truncations of the Plefka expansion of the Gibbs free energy. The Bethe free energy is introduced and rewritten as a Gibbs free energy. From there ..."
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Inference in Boltzmann machines is NPhard in general. As a result approximations are often necessary. We review the mean field and TAP approximations as truncations of the Plefka expansion of the Gibbs free energy. The Bethe free energy is introduced and rewritten as a Gibbs free energy. From
Probabilistic Model and Belief Propagation Probabilistic Information Processing Probabilistic Models Bayes Formulas Belief Propagation =Bethe Approximation
, 2013
"... jiij ffUP,f jk jkj jf jiij iji fMffU fM Constant V: Set of all the nodes (vertices) in graph G E: Set of all the links (edges) in graph G j i), ( EVG ..."
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jiij ffUP,f jk jkj jf jiij iji fMffU fM Constant V: Set of all the nodes (vertices) in graph G E: Set of all the links (edges) in graph G j i), ( EVG
Probabilistic Model and Belief Propagation Probabilistic Information Processing Probabilistic Models Bayes Formulas Belief Propagation =Bethe Approximation
"... 1 Bayesian image modeling and phase transition in generalized sparse Markov random fields and loopy belief propagation Kazuyuki Tanaka ..."
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1 Bayesian image modeling and phase transition in generalized sparse Markov random fields and loopy belief propagation Kazuyuki Tanaka
Probabilistic Information Processing Probabilistic Models Bayes Formulas Belief Propagation =Bethe Approximation Bayesian Networks
"... Eji jiij ffUP,f jk jkj jf jiij iji fMffU fM Constant V: Set of all the nodes (vertices) in graph G E: Set of all the links (edges) in graph G ..."
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Eji jiij ffUP,f jk jkj jf jiij iji fMffU fM Constant V: Set of all the nodes (vertices) in graph G E: Set of all the links (edges) in graph G
Bethe and Related Pairwise Entropy Approximations
"... For undirected graphical models, belief propagation often performs remarkably well for approximate marginal inference, and may be viewed as a heuristic to minimize the Bethe free energy. Focusing on binary pairwise models, we demonstrate that several recent results on the Bethe approximation ma ..."
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For undirected graphical models, belief propagation often performs remarkably well for approximate marginal inference, and may be viewed as a heuristic to minimize the Bethe free energy. Focusing on binary pairwise models, we demonstrate that several recent results on the Bethe approximation
Approximating the Bethe partition function
"... When belief propagation (BP) converges, it does so to a stationary point of the Bethe free energy F, and is often strikingly accurate. However, it may converge only to a local optimum or may not converge at all. An algorithm was recently introduced by Weller and Jebara for attractive binary pairwise ..."
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Cited by 4 (3 self)
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better performance and, for attractive models, yields a fully polynomialtime approximation scheme (FPTAS) without any degree restriction. Further, our methods apply to general (nonattractive) models, though with no polynomial time guarantee in this case, demonstrating that approximating log of the Bethe
Results 11  20
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474