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提出基于均值场计算树的Ising图模型消息族传播算法.首先定义Ising图模型均值场计算树和均值场剪枝计算树概念来描述Ising图模型均值场推理方法的迭代计算过程.然后基于均值场计算树设计Ising图模型消息族传播算法,指出沿着计算树自底向上逐层进行消息族传播,可计算根节点变量的边缘概率分布族.同时证明基于均值场剪枝计算树的消息族传播算法可计算出变量边缘概率分布的界,即此时的边缘概率分布族包括边缘概率分布精确值.最后通过数值实验验证消息族传播算法的有效性和边缘概率分布界的紧致性.
This paper proposes a message family propagation algorithm based on the mean value field calculation tree of Ising graph model.Firstly, we define the concept of tree calculation of the mean value field calculation tree and the mean field pruning calculation tree of Ising graph model to describe the iterative calculation process of the mean field reasoning method of Ising graph model.And then, We calculate the message propagation algorithm of tree design Ising graph model and point out that the distribution of edge probabilities of root node variables can be calculated from bottom to top along the calculation tree.At the same time, The algorithm can calculate the boundary of the probability distribution of the edge of the variable, that is, the edge probability distribution at this time includes the exact value of the edge probability distribution.Finally, the validity of the message family propagation algorithm and the compactness of the edge probability distribution boundary are verified by numerical experiments.