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Complexity of Bethe approximation
 In Artificial Intelligence and Statistics
, 2012
"... This paper resolves a common complexity issue in the Bethe approximation of statistical physics and the sumproduct Belief Propagation (BP) algorithm of artificial intelligence. The Bethe approximation reduces the problem of computing the partition function in a graphical model to that of solving a ..."
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Cited by 5 (0 self)
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This paper resolves a common complexity issue in the Bethe approximation of statistical physics and the sumproduct Belief Propagation (BP) algorithm of artificial intelligence. The Bethe approximation reduces the problem of computing the partition function in a graphical model to that of solving a
What Cannot be Learned with Bethe Approximations
"... We address the problem of learning the parameters in graphical models when inference is intractable. A common strategy in this case is to replace the partition function with its Bethe approximation. We show that there exists a regime of empirical marginals where such Bethe learning will fail. By fai ..."
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Cited by 13 (1 self)
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We address the problem of learning the parameters in graphical models when inference is intractable. A common strategy in this case is to replace the partition function with its Bethe approximation. We show that there exists a regime of empirical marginals where such Bethe learning will fail
Counting independent sets using the Bethe approximation
 SIAM J. Discr. Math
, 2011
"... Abstract. We consider the #Pcomplete problem of counting the number of independent sets in a given graph. Our interest is in understanding the effectiveness of the popular belief propagation (BP) heuristic. BP is a simple iterative algorithm that is known to have at least one fixed point, where eac ..."
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Cited by 12 (3 self)
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point) leads to the Bethe approximation for the number of independent sets of the given graph. BP is not known to converge in general, nor is an efficient, convergent procedure for finding stationary points of the Bethe free energy known. Furthermore, the effectiveness of the Bethe approximation
How to compute loop corrections to the Bethe approximation
 Journal of Statistical Mechanics
, 2005
"... We introduce a method for computing corrections to Bethe approximation for spin models on arbitrary lattices. Unlike cluster variational methods, the new approach takes into account fluctuations on all length scales. The derivation of the leading correction is explained and applied to two simple exa ..."
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Cited by 17 (0 self)
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We introduce a method for computing corrections to Bethe approximation for spin models on arbitrary lattices. Unlike cluster variational methods, the new approach takes into account fluctuations on all length scales. The derivation of the leading correction is explained and applied to two simple
Bethe Approximation for a Semiflexible Polymer Chain
, 2008
"... We present a Bethe approximation to study lattice models of linear polymers. The approach is variational in nature and based on the cluster variation method (CVM). We focus on a model with (i) a nearest neighbor attractive energy ǫv between pair of non–bonded monomers, (ii) a bending energy ǫh for e ..."
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We present a Bethe approximation to study lattice models of linear polymers. The approach is variational in nature and based on the cluster variation method (CVM). We focus on a model with (i) a nearest neighbor attractive energy ǫv between pair of non–bonded monomers, (ii) a bending energy ǫh
Bethe Approximation for SelfInteracting Lattice Trees
, 2008
"... In this paper we develop a Bethe approximation, based on the cluster variation method, which is apt to study lattice models of branched polymers. We show that the method is extremely accurate in cases where exact results are known as, for instance, in the enumeration of spanning trees. Moreover, the ..."
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In this paper we develop a Bethe approximation, based on the cluster variation method, which is apt to study lattice models of branched polymers. We show that the method is extremely accurate in cases where exact results are known as, for instance, in the enumeration of spanning trees. Moreover
CSMA using the Bethe Approximation: Scheduling and Utility Maximization
, 2013
"... CSMA (Carrier Sense Multiple Access), which resolves contentions over wireless networks in a fully distributed fashion, has recently gained a lot of attentions since it has been proved that appropriate control of CSMA parameters guarantees optimality in terms of stability (i.e., scheduling) and syst ..."
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, for the stability problem, the proposed distributed algorithm requires, somewhat surprisingly, only one iteration among links. Our approach is motivated by the Bethe approximation (introduced by Yedidia, Freeman and Weiss in 2005) allowing us to express approximate solutions via a certain nonlinear system
Minimization of Continuous Bethe Approximations: A Positive Variation
"... We develop convergent minimization algorithms for Bethe variational approximations which explicitly constrain marginal estimates to families of valid distributions. While existing message passing algorithms define fixed point iterations corresponding to stationary points of the Bethe free energy, th ..."
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Cited by 2 (0 self)
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We develop convergent minimization algorithms for Bethe variational approximations which explicitly constrain marginal estimates to families of valid distributions. While existing message passing algorithms define fixed point iterations corresponding to stationary points of the Bethe free energy
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
New generalizations of the Bethe approximation via asymptotic expansion
 in Proc. IEICE Symp. Inf. Theory App., Oita, Japan, Dec. 11–14 2012. [Online]. Available: http://arxiv.org/abs/1210.2592
"... ar ..."
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