arXiv 1301.06052013-01cs.AI

循环信念传播与Gibbs测度

Loopy Belief Propogation and Gibbs Measures

University of California, Berkeley（加州大学伯克利分校）

Sekhar Tatikonda, Michael I. Jordan

备注：: Appears in Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence (UAI2002)

摘要：

我们解决的问题，在循环的信念传播（LBP）算法的收敛性。具体地说，我们把LBP的收敛性与定义在LBP的相关计算树上的Gibbs测度序列的弱极限的存在性联系起来.利用Gibbs测度理论的工具，我们得到了易于检验的收敛性充分条件. LBP的收敛性的失败意味着相关Gibbs规范的多个阶段的存在.这些结果为算法的机制提供了新的见解.

英文摘要：

We address the question of convergence in the loopy belief propagation (LBP) algorithm. Specifically, we relate convergence of LBP to the existence of a weak limit for a sequence of Gibbs measures defined on the LBP s associated computation tree.Using tools FROM the theory OF Gibbs measures we develop easily testable sufficient conditions FOR convergence.The failure OF convergence OF LBP implies the existence OF multiple phases FOR the associated Gibbs specification.These results give new insight INTO the mechanics OF the algorithm.

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