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CORR
2010
Springer

Graph Zeta Function in the Bethe Free Energy and Loopy Belief Propagation

9 years 9 months ago
Graph Zeta Function in the Bethe Free Energy and Loopy Belief Propagation
We propose a new approach to the analysis of Loopy Belief Propagation (LBP) by establishing a formula that connects the Hessian of the Bethe free energy with the edge zeta function. The formula has a number of theoretical implications on LBP. It is applied to give a sufficient condition that the Hessian of the Bethe free energy is positive definite, which shows non-convexity for graphs with multiple cycles. The formula clarifies the relation between the local stability of a fixed point of LBP and local minima of the Bethe free energy. We also propose a new approach to the uniqueness of LBP fixed point, and show various conditions of uniqueness.
Yusuke Watanabe, Kenji Fukumizu
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Yusuke Watanabe, Kenji Fukumizu
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