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• W1569289728 abstract "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. The proposed approach is applicable to a wide class of models including multinomial and Gaussian types. The connection derives a number of new theoretical results on LBP and BFE. This paper focuses two of such topics. One is the analysis of the region where the Hessian of the Bethe free energy is positive definite, which derives the non-convexity of BFE for graphs with multiple cycles, and a condition of convexity on a restricted set. This analysis also gives a new condition for the uniqueness of the LBP fixed point. The other result is to clarify the relation between the local stability of a fixed point of LBP and local minima of the BFE, which implies, for example, that a locally stable fixed point of the Gaussian LBP is a local minimum of the Gaussian Bethe free energy." @default.
• W1569289728 created "2016-06-24" @default.
• W1569289728 creator A5012922872 @default.
• W1569289728 creator A5022744391 @default.
• W1569289728 date "2011-03-03" @default.
• W1569289728 modified "2023-09-27" @default.
• W1569289728 title "Loopy Belief Propagation, Bethe Free Energy and Graph Zeta Function" @default.
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• W1569289728 hasPublicationYear "2011" @default.
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