线性混合效应模型贝叶斯分位回归的变分推断  

Variational Inference of Bayesian Quantile Regression in Linear Mixed Effect Model

作　　者：王维贤 殷先军[1] 张娟娟 田茂再[3,4] WANG Weixian;YIN Xianjun;ZHANG Juanjuan;TIAN Maozai(School of Statistics and Mathematics,Central University of Finance and Economics,Beijing 102206;School of Economics and Trade,College of Guangzhou Huashang,Guangzhou 511399;Center for Applied Statistics,School of Statistics,Renmin University of China,Beijing 100872;School of Statistics and Data Science,Xinjiang University of Finance,Urumqi 830012)

机构地区：[1]中央财经大学统计与数学学院,北京102206 [2]广州华商学院经济贸易学院,广州511399 [3]中国人民大学应用统计科学研究中心,中国人民大学统计学院,北京100872 [4]新疆财经大学统计与数据科学学院,乌鲁木齐830012

出　　处：《系统科学与数学》2024年第1期269-284,共16页Journal of Systems Science and Mathematical Sciences

基　　金：中国人民大学科学研究基金(中央高校基本科研业务费专项资金资助)(22XNL016)资助课题.

摘　　要：贝叶斯分位回归能够对线性混合效应模型中的参数进行良好的估计.在贝叶斯参数估计中,常用Gibbs抽样方法.为了得到精确的估计结果,Gibbs抽样方法需要进行多次抽样.当模型参数维度较高时,Gibbs抽样方法将会十分耗时.因此,文章采用变分推断来近似参数的后验分布.变分推断采用无条件分布来逼近Gibbs方法得到的条件分布,从而使得计算变得高效.文章将模型参数的先验假定为正态分布,对无惩罚线性混合效应模型的参数进行变分推断.考虑到模型参数可能面临的高维情况,文章将模型参数的先验假定为Laplace分布,对双惩罚线性混合效应模型的参数也进行变分推断.从模拟结果来看,变分推断对模型参数估计的精度虽略小于Gibbs抽样方法,但其运行速度较快.在高维情况下,运行效率依然很高.在大数据时代,时间和资源的消耗是文章首先需要考虑的因素.因此,文章提出的方法可实际运用在高维线性混合效应模型中.Bayesian quantile regression can well estimate the parameters in the linear mixed effect model.Gibbs sampling is commonly used in Bayesian parameter estimation.In order to obtain accurate estimation results,Gibbs sampling method requires multiple sampling.When the model parameter dimension is high,the Gibbs sampling will be very time-consuming.Therefore,we use variational inference to approximate the posterior distribution of parameters.Variational inference uses unconditional distribution to approximate the conditional distribution obtained by Gibbs method,thus making the calculation more efficient.In this paper,a priori assumption of the parameters of the model is normal distribution,and the variation inference of the parameters of the unpunished linear mixed effect model is carried out.Considering the high dimensional situation,we assume the prior distribution of the model parameters as Laplace distribution,and make variational inference for the parameters of the double penalty linear mixed effect model.From the simulation results,although the accuracy of variational inference for model parameter estimation is slightly less than that of Gibbs sampling,it runs faster.In the case of high dimension,the improvement of operation efficiency is more obvious.In the era of big data,the consumption of time and resources is the first factor we need to consider.Therefore,the method proposed in this paper can be applied to the high-dimensional linear mixed effect model.

关 键 词：贝叶斯分位回归 线性混合效应模型 GIBBS抽样 变分推断 

分 类 号：O212.1[理学—概率论与数理统计]