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

Citations: | 21 - 7 self |

### BibTeX

@MISC{Hazan_norm-productbelief,

author = {Tamir Hazan and Amnon Shashua},

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

year = {}

}

### OpenURL

### Abstract

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 messagepassing 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