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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
Effective Energy Function for Proteins in Solution
, 1999
"... A Gaussian solventexclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. ..."
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Cited by 259 (16 self)
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A Gaussian solventexclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution
A New Class of Upper Bounds on the Log Partition Function
 In Uncertainty in Artificial Intelligence
, 2002
"... Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis [11, 5, 4]. We introduce a new class of upper bounds on the log partition function, based on convex combinations of distribution ..."
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Cited by 225 (32 self)
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of distributions in the exponential domain, that is applicable to an arbitrary undirected graphical model. In the special case of convex combinations of treestructured distributions, we obtain a family of variational problems, similar to the Bethe free energy, but distinguished by the following desirable
Complete suboptimal folding of RNA and the stability of secondary structures
 BIOPOLYMERS 49:145–165
, 1999
"... An algorithm is presented for generating rigorously all suboptimal secondary structures between the minimum free energy and an arbitrary upper limit. The algorithm is particularly fast in the vicinity of the minimum free energy. This enables the efficient approximation of statistical quantities, s ..."
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Cited by 215 (23 self)
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An algorithm is presented for generating rigorously all suboptimal secondary structures between the minimum free energy and an arbitrary upper limit. The algorithm is particularly fast in the vicinity of the minimum free energy. This enables the efficient approximation of statistical quantities
Autoencoders, Minimum Description Length and Helmholtz Free Energy
, 1994
"... An autoencoder network uses a set of recognition weights to convert an input vector into a code vector. It then uses a set of generative weights to convert the code vector into an approximate reconstruction of the input vector. We derive an objective function for training autoencoders based on the M ..."
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Cited by 140 (11 self)
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An autoencoder network uses a set of recognition weights to convert an input vector into a code vector. It then uses a set of generative weights to convert the code vector into an approximate reconstruction of the input vector. We derive an objective function for training autoencoders based
Bethe free energy, Kikuchi approximations and belief propagation algorithms
, 2000
"... Belief propagation (BP) was only supposed to work for treelike networks but works surprisingly well in many applications involving networks with loops, including turbo codes. However, there has been little understanding of the algorithm or the nature of the solutions it nds for general graphs. ..."
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Cited by 95 (2 self)
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. We show that BP can only converge to a stationary point of an approximate free energy, known as the Bethe free energy in statistical physics. This result characterizes BP xedpoints and makes connections with variational approaches to approximate inference. More importantly, our analysis lets us
A DoubleLoop Algorithm to Minimize the Bethe and Kikuchi Free Energies
 NEURAL COMPUTATION
, 2001
"... Recent work (Yedidia, Freeman, Weiss [22]) has shown that stable points of belief propagation (BP) algorithms [12] for graphs with loops correspond to extrema of the Bethe free energy [3]. These BP algorithms have been used to obtain good solutions to problems for which alternative algorithms fail t ..."
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Cited by 137 (5 self)
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approximation which includes the Bethe free energy as a special case [3]. (Yedidia et al [22] showed that a \generalized belief propagation" algorithm also has its xed points at extrema of the Kikuchi free energy). We are able both to obtain a dual formulation for Kikuchi but also obtain a double
Broken replica symmetry bounds in the mean field spin glass model
 Comm. Math Phys
, 2003
"... By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the SherringtonKirkpatrick model, and the Derrida pspin model. Here we extend this argument in order to compare the limiting free energy w ..."
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Cited by 146 (15 self)
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expressions is given in the form of a sum rule, extending our previous work on the comparison between the true free energy and its replica symmetric SherringtonKirkpatrick approximation. We give also a variational bound for the infinite volume limit of the ground state energy per site.
Approximate inference and constrained optimization
 In 19th UAI
, 2003
"... Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms correspond to extrema of the Bethe and Kikuchi free energy (Yedidia et al., 2001). However, belief propagation does not always con ..."
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Cited by 62 (9 self)
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Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms correspond to extrema of the Bethe and Kikuchi free energy (Yedidia et al., 2001). However, belief propagation does not always
Results 1  10
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1,978