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We propose a new approach to the theoretical analysis of Loopy Belief Propagation (LBP) and the Bethe free energy (BFE) by establishing a formula to connect LBP and BFE with a graph zeta function.
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Learning in graphical models
M.I. Jordan · 1998
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Turbo decoding as an instance of Pearl’s ”belief propagation” algorithm
R.J. McEliece, D.J.C. MacKay, and J.F. Cheng · 1998
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A note on the zeta function of a graph
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A combinatorial proof of Bass’s evaluations of the Ihara-Selberg zeta function for graphs
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Loopy belief propagation for approximate inference: An empirical study
K. Murphy, Y. Weiss, and M.I. Jordan · 1999
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Zeta functions of finite graphs
M. Kotani and T. Sunada · 2000
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Correctness of local probability propagation in graphical models with loops
Y. Weiss · 2000
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Factor graphs and the sum-product algorithm
F.R. Kschischang, B.J. Frey, and H.A. Loeliger · 2001
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Generalized belief propagation
J.S. Yedidia, W.T. Freeman, and Y. Weiss · 2001
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Stable fixed points of loopy belief propagation are minima of the Bethe free energy
T. Heskes · 2002
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Analytic and algorithmic solution of random satisfiability problems
M. Mezard, G. Parisi, and R. Zecchina · 2002
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Belief propagation and statistical physics
P. Pakzad and V. Anantharam · 2002
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Constructing free-energy approximations and generalized belief propagation algorithms
J.S. Yedidia, W.T. Freeman, and Y. Weiss · 2005
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Loopy belief propagation: Convergence and effects of message errors
A.T. Ihler, J.W. Fisher III, and A.S. Willsky · 2006
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Bartholdi zeta functions for hypergraphs
S. Iwao · 2006
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Walk-sum interpretation and analysis of Gaussian belief propagation
J. Johnson, D. Malioutov, and A. Willsky · 2006
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Walk-sums and belief propagation in Gaussian graphical models
D.M. Malioutov, J.K. Johnson, and A.S. Willsky · 2006
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The zeta function of a hypergraph
C.K. Storm · 2006
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Graphical models in applied multivariate statistics
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Bayesian compressive sensing via belief propagation
D. Baron, S. Sarvotham, and R.G. Baraniuk · 2010
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Discrete geometric analysis of message passing algorithm on graphs
Y Watanabe · 2010
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On the uniquness of the solution of belief propagation equation
W. Watanabe and K. Fukumizu · 2011
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