基于Ising计算树的均值场区间传播算法

Mean Field Interval Propagation Algorithm Based on Ising Computation Tree

基于不完全泛函迭代,设计一个均值场区间传播算法,可给出变量期望界.首先,定义Ising均值场计算树模型来表示Ising均值场迭代计算过程.然后,基于Ising计算树设计均值场区间传播算法,通过在计算树上进行消息区间传播,计算出根变量簇变量期望区间.同时证明在2层计算树上区间传播算法给出的变量期望区间包含期望精确值,即给出变量期望界.最后,通过对比实验验证该算法的有效性和期望界的紧致性.

A mean filed interval propagation algorithm is designed based on incomplete functional iterations. This algorithm can yield the expectation bound of variables. Firstly, a concept of computation tree is proposed to reveal the iteration computation process of Ising mean field. Then, a mean field interval propagation algorithm based on the Ising computation tree is put forward, which propagates message intervals through the computation tree and presents the mean intervals of random variables in root node. It is proved that the variable mean interval computed by the interval propagation algorithm with 2-layer computation tree contains the exact value, called the mean bound of random variable. Finally, theoretical and experimental results show that the interval propagation algorithm is valid and the mean bound is tight.