基于平均场近似的BP算法求解随机块模型  

A mean-field approximation based BP algorithm for solving the stochastic block model

作　　者：马闯 杨晓龙 陈含爽[2] 张海峰[3] Ma Chuang;Yang Xiao-Long;Chen Han-Shuang;Zhang Hai-Feng(School of Internet,Anhui University,Hefei 230039,China;School of Physics and Material Science,Anhui University,Hefei 230601,China;School of Mathematical Science,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学互联网学院,合肥230039 [2]安徽大学物理与材料科学学院,合肥230601 [3]安徽大学数学科学学院,合肥230601

出　　处：《物理学报》2021年第22期339-350,共12页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12005001,61973001,11875069);安徽省高校协同创新项目(批准号:GXXT-2021-032);安徽省自然科学基金(批准号:2008085QF299)资助的课题.

摘　　要：置信传播(BP)算法作为推断概率图模型的主流算法是求解随机块模型中联合概率分布的重要方法之一.但现有的方法要么在处理核边结构问题上存在精度不足问题,要么在理论的推导上存在近似太多,导致求解过程复杂且难以理解问题,或两个问题均存在.当然,精度不足也是由近似多造成的.导致理论近似多且推导复杂的主要原因,是随机块模型推断过程中求解联合概率分布并不是直接套用BP算法,即处理的图(网络)与概率图模型的图不统一.因此,本文利用平均场近似修正联合概率分布,使其完全匹配BP算法的迭代公式,这样使得在理论推导上简单易懂.最后通过实验验证,该方法是有效的.As a mainstream algorithm for inferring probabilistic graphical models,belief propagation(BP)algorithm is one of the most important methods to solve the joint probability distribution in the stochastic block model.However,existing methods either lead to low accuracy in dealing with the core-periphery structure problem,or the theoretical derivation is difficult to understand due to a large number of approximation,or both exist.Of course,the reason for low accuracy comes from too many approximations.The main reason for many approximations and complex theoretical derivation is that the joint probability distribution in the inference process of the stochastic block model is not directly solved by the BP algorithm,that is,the graph(network)being processed is not consistent with the graph considered in the probabilistic graph model.Therefore,in this paper,a mean-field approximation is developed to modify the joint probability distribution to make the BP algorithm match perfectly,which makes the theoretical derivation easy to understand.Finally,the effectiveness of the proposed method is validated by the experimental results.

关 键 词：随机块模型 置信传播算法 联合概率分布 平均场近似 

分 类 号：O157.5[理学—数学]