基于变分贝叶斯推断的因子分析法  

Factor analysis based on variational Bayes inference

作　　者：巴丽伟 童常青 BA Liwei;TONG Changqing(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2022年第3期95-102,共8页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家社会科学基金资助项目(18BTJ026)。

摘　　要：为了讨论因子分析模型中超先验分布对变分贝叶斯估计结果的影响。首先,引入贝叶斯理论进行因子分析,提出因子分析模型的变分贝叶斯推断算法;然后,运用提出的算法对模型参数进行估计,并根据变分贝叶斯信息准则(Variational Bayes Information Criterion,VBIC)进行模型选择;最后,应用于合成数据集。实验结果表明,大约有90%的偏差绝对值小于0.1,证明了该算法的有效性;与参数未设置超先验分布相比,当参数设置超先验分布时,VBIC值减少,模型的参数估计效果更佳。This paper is to discuss the influence of the super-prior distribution in the factor analysis model on the results of the variational Bayes estimation.Firstly,we introduce Bayes theory to perform factor analysis,and propose a variational Bayes inference algorithm for factor analysis models;then,we use the proposed algorithm to estimate model parameters,and select the model according to the variational Bayes information criterion(Variational Bayes Information Criterion,VBIC);finally,it is applied to the synthetic data set.Experimental results show that about 90% of the absolute deviations are less than 0.1,which proves the effectiveness of the algorithm;and compared with the parameter setting without super-priori,when the parameters are set with super-priori,the VBIC value is decreases,and the model's parameter estimation effect better.

关 键 词：变分贝叶斯推断 因子分析 参数估计 模型选择 VBIC准则 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]