Computer Science – Artificial Intelligence
Scientific paper
2010-02-17
Advances in Neural Information Processing Systems 22, pages 2017-2025
Computer Science
Artificial Intelligence
19 pages, Annual Conference on Neural Information Processing Systems (NIPS 2009), together with the supplementary material
Scientific paper
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.
Fukumizu Kenji
Watanabe Yusuke
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