Graph zeta function and loopy belief propagation

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) byestablishing a formula that connects the Hessian of the Bethe free energy with theedge 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 energyis positive definite, which shows non-convexity for...

Loopy Belief Propagation, Bethe Free Energy and Graph Zeta Function

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 tw...

Uniqueness of Belief Propagation on Signed Graphs

While loopy Belief Propagation (LBP) has been utilized in a wide variety of applications with empirical success, it comes with few theoretical guarantees. Especially, if the interactions of random variables in a graphical model are strong, the behaviors of the algorithm can be difficult to analyze due to underlying phase transitions. In this paper, we develop a novel approach to the uniqueness ...

The Loopy Belief Propagation for Factor Graphs

Correctness of Belief Propagation in Gaussian Graphical Models of Arbitrary Topology Correctness of Belief Propagation in Gaussian Graphical Models of Arbitrary Topology

Graphical models, such as Bayesian networks and Markov random elds represent statistical dependencies of variables by a graph. Local \belief propagation" rules of the sort proposed by Pearl [20] are guaranteed to converge to the correct posterior probabilities in singly connected graphs. Recently good performance has been obtained by using these same rules on graphs with loops, a method known a...