## Norm-Product Belief Propagation: Primal-Dual Message-Passing for Approximate Inference (2008)

Citations: | 21 - 7 self |

### BibTeX

@MISC{Hazan08norm-productbelief,

author = {Tamir Hazan and Amnon Shashua},

title = {Norm-Product Belief Propagation: Primal-Dual Message-Passing for Approximate Inference},

year = {2008}

}

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### OpenURL

### Abstract

Inference problems in graphical models can be represented as a constrained optimization of a free energy function. In this paper we treat both forms of probabilistic inference, estimating marginal probabilities of the joint distribution and finding the most probable assignment, through a unified message-passing algorithm architecture. In particular we generalize the Belief Propagation (BP) algorithms of sum-product and maxproduct and tree-rewaighted (TRW) sum and max product algorithms (TRBP) and introduce a new set of convergent algorithms based on ”convex-free-energy” and Linear-Programming (LP) relaxation as a zero-temprature of a convex-free-energy. The main idea of this work arises from taking a general perspective on the existing BP and TRBP algorithms while observing that they all are reductions from the basic optimization formula of f + ∑ i hi