基于变分贝叶斯推断的因子分析法

Factor analysis based on variational Bayes inference

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.